Russian paratroopers landed in the city of Kharkiv early Wednesday morning after Russian forces escalated their attacks on crowded urban areas the day before in what Ukraine's leader called a blatant campaign of terror, while US President Joe Biden vowed to make his Russian counterpart "pay a price" for the invasion.
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"Nobody will forgive. Nobody will forget," Ukraine's President Volodymyr Zelenskyy vowed after the bloodshed on the central square in Kharkiv, the country's second-largest city, and the deadly bombing of a TV tower in the capital.
The agency stated that the Russian soldiers attacked a military medical center, noting that a "battle broke out between the invaders and the Ukrainian defenders."
Biden used his first State of the Union address to highlight the resolve of a reinvigorated Western alliance that has worked to rearm the Ukrainian military and adopt tough sanctions, which he said have left Russian President Vladimir Putin "isolated in the world more than he has ever been."
"Throughout our history, we've learned this lesson – when dictators do not pay a price for their aggression, they cause more chaos," Biden said. "They keep moving. And the costs and threats to America and the world keep rising."
Biden devoted the first 12 minutes of his Tuesday evening address to Ukraine, with lawmakers of both parties repeatedly rising to their feet and applauding as he praised the bravery of Ukraine's people and condemned Putin's assault.

As Biden spoke, a 40-mile (64-kilometer) convoy of hundreds of Russian tanks and other vehicles advanced slowly on Kyiv, the capital city of nearly 3 million people, in what the West feared was a bid by Putin to topple the government and install a Kremlin-friendly regime.
The invading forces also pressed their assault on other towns and cities, including the strategic ports of Odesa and Mariupol in the south.
Day 6 of the biggest ground war in Europe since World War II found Russia increasingly isolated, beset by the sanctions that have thrown its economy into turmoil and left the country practically friendless, apart from a few nations like China, Belarus and North Korea.
As the fighting in Ukraine raged, the death toll remained unclear. One senior Western intelligence official estimated that more than 5,000 Russian soldiers had been captured or killed. Ukraine gave no overall estimate of troop losses.
The UN human rights office said it has recorded 136 civilian deaths. The real toll is believed to be far higher.
Britain's Defense Ministry said it had seen an increase in Russian air and artillery strikes on populated urban areas over the past two days. It also said three cities – Kharkiv, Kherson and Mariupol – were encircled by Russian forces.
Many military experts worry that Russia may be shifting tactics. Moscow's strategy in Chechnya and Syria was to use artillery and air bombardments to pulverize cities and crush fighters' resolve.
Ukrainian authorities said five people were killed in the attack on the TV tower, which is near central Kyiv and a short walk from numerous apartment buildings. A TV control room and power substation were hit, and at least some Ukrainian channels briefly stopped broadcasting, officials said.
The bombing came after Russia announced it would target transmission facilities used by Ukraine's intelligence agency. It urged people living near such places to leave their homes.
Zelenskyy's office also reported a missile attack on the site of the Babi Yar Holocaust memorial, near the tower. A spokesman for the memorial said a Jewish cemetery at the site, where Nazi occupiers murdered more than 33,000 Jews over two days in 1941, was damaged.
In Kharkiv, with a population of about 1.5 million, at least six people were killed when the region's Soviet-era administrative building on Freedom Square was hit with what was believed to be a missile.
The Slovenian Foreign Ministry said its consulate in Kharkiv, located in another large building on the square, was destroyed in the attack.
The attack on Freedom Square – Ukraine's largest plaza, and the nucleus of public life in the city – was seen by many Ukrainians as brazen evidence that the Russian invasion wasn't just about hitting military targets but also about breaking their spirit.
The bombardment blew out windows and walls of buildings that ring the massive square, which was piled high with debris and dust. Inside one building, chunks of plaster were scattered, and doors, ripped from their hinges, lay across hallways.

"People are under the ruins. We have pulled out bodies," said Yevhen Vasylenko, an emergency official.
Zelenskyy pronounced the attack on the square "frank, undisguised terror" and a war crime. "This is state terrorism of the Russian Federation," he said.
In an emotional appeal to the European Parliament later, Zelenskyy said: "We are fighting also to be equal members of Europe. I believe that today we are showing everybody that is what we are."
Another Russian airstrike hit a residential area in the city of Zhytomyr, the town's mayor said. Ukraine's emergency services said Tuesday's strike killed at least two people, set three homes on fire and broke the windows in a nearby hospital. About 85 miles (140 kilometers) west of Kyiv, Zhytomyr is the home of the elite 95th Air Assault Brigade, which may have been the intended target.
Zelenskyy said 16 children had been killed around Ukraine on Monday, and he mocked Russia's claim that it is going after only military targets.
"Where are the children? What kind of military factories do they work at? What tanks are they going at?" Zelenskyy said.
Human Rights Watch said it documented a cluster bomb attack outside a hospital in Ukraine's east in recent days. Residents also reported the use of such weapons in Kharkiv and Kiyanka village. The Kremlin denied using cluster bombs.
Cluster bombs shoot smaller "bomblets" over a large area, many of which fail to explode until long after they've been dropped. If their use is confirmed, that would represent a new level of brutality in the war and could lead to further isolation of Russia.
The first talks between Russia and Ukraine since the invasion were held Monday but ended with only an agreement to talk again. On Tuesday, Zelenskyy said Russia should stop bombing first.
"As for dialogue, I think yes, but stop bombarding people first and start negotiating afterward," he told CNN in an interview in a heavily guarded government compound.
He urged NATO members to impose a no-fly zone to stop the Russian air force, saying this would be a preventative measure and not meant to drag the alliance into war with Russia.

Zelenskyy, who has refused offers to leave the Ukrainian capital as Russian forces advanced, also said Ukraine would demand legally binding security guarantees if NATO shut the door on Ukraine's membership prospects.
"This is not about dragging NATO countries into war. The truth is everyone has long since been dragged into war and definitely not by Ukraine, but by Russia – a large-scale war is going on," Zelenskyy said.
He added, however, that Biden had personally conveyed to him that now was not the time to introduce such a measure.
Ukraine has pressed NATO to accelerate its entry, a move fiercely opposed by Russia and cited as one of Moscow's reasons for launching its campaign.
"Our partners, if they are not ready to take Ukraine into NATO ... because Russia does not want Ukraine to be in NATO, should work out common security guarantees for Ukraine," Zelenskiy said.
"This means that we have our territorial integrity, that our borders are protected, we have special relations with all our neighbors, we are completely safe, and the guarantors that give us security, they guarantee this legally," he said.
In his speech, Biden announced that the US was joining several other countries in closing its airspace to Russian planes. He also warned the country's oligarchs that the Department of Justice was assembling a task force to investigate any crimes they committed.
"We are joining with our European allies to find and seize your yachts, your luxury apartments, your private jets," he said. "We are coming for your ill-begotten gains."
Biden trumpeted the toll global measures had taken on the Russian economy already, including a stock market plunge and currency devaluation.
US Ambassador to Israel Thomas Nides on Tuesday called the war in Ukraine "a tragedy."
"Putin is a mad man; sadly, thousands will die and millions will flee, which will create the largest refugee crisis in Europe in 40 years, if not more," he said at a meeting of ambassadors held at the Jewish People Policy Institute headquartered in Jerusalem.
Nides added that he "doesn't think any of use predicted this would happen. Many of us believed this would never happen and that no one would be so crazy, that it was just one big bluff."
As for the sanctions against Putin, he said: "In my opinion, for the first time in a long time we're seeing the world speak in one voice, and this isn't just a message to Putin, but to others in the world considering doing bad things. This won't stop Putin from killing people, but the consequences for Russia and the Russian people will be significant and our enemies will be watching closely."

Moscow, meanwhile, made new threats of escalation, days after raising the specter of nuclear war. A top Kremlin official warned that the West's "economic war" against Russia could turn into a "real one."
Inside Russia, a top radio station critical of the Kremlin was taken off the air after authorities threatened to shut it down over its coverage of the invasion. Among other things, the Kremlin is not allowing the fighting to be referred to as an "invasion" or "war."
Roughly 660,000 people have fled Ukraine, and countless others have taken shelter underground. Bomb damage has left hundreds of thousands of families without drinking water, UN humanitarian coordinator Martin Griffiths said.
"It is a nightmare, and it seizes you from the inside very strongly. This cannot be explained with words," said Kharkiv resident Ekaterina Babenko, taking shelter in a basement with neighbors for a fifth straight day. "We have small children, elderly people, and frankly speaking it is very frightening."
A Ukrainian military official said Belarusian troops joined the war Tuesday in the Chernihiv region in the north, without providing details. But just before that, Belarusian President Alexander Lukashenko said his country had no plans to join the fight.
A senior US defense official said that Russia's military progress – including by the massive convoy – has slowed, plagued by logistical and supply problems. Some Russian military columns have reportedly run out of gas and food, the official said, and morale has suffered as a result.
Overall, the Russian military has been stalled by fierce resistance on the ground and a surprising inability to completely dominate Ukraine's airspace.
The immense convoy, with vehicles packed together along narrow roads, would seemingly be "a big fat target" for Ukrainian forces, the senior Western intelligence official said on condition of anonymity.
"But it also shows you that the Russians feel pretty comfortable being out in the open in these concentrations because they feel that they're not going to come under air attack or rocket or missile attack," the official said.
"Looking at the Russian operation so far, they're having tremendous problems with logistics and communications. The whole effort seems shambolic," Michael Kofman, an expert on the Russian military at Washington's Wilson Center, wrote in a tweet.
Many Western military analysts fear that Russia will now fall back on tactics, which call for crushing bombardment of built-up areas before trying to enter them.
A senior US defense official, speaking on condition of anonymity, said:
"One reason why things appear to be stalled north of Kyiv is that the Russians themselves are regrouping and rethinking and trying to adjust to the challenges that they've had."

The Russians have been surprised not only by the scale of Ukrainian resistance but also by poor morale among their own forces, some of whom surrendered without a fight, the official said, without providing evidence.
Russia still has more forces to throw into the fight, though.
Russia's Defense Minister Sergei Shoigu said the "special military operation" would continue until it had achieved its goals, defined by Putin as disarming Ukraine and capturing the "neo-Nazis" he says are running the country.
Russian Foreign Minister Sergei Lavrov told a Geneva disarmament meeting via video link that Ukraine had been seeking nuclear weapons. He did not provide evidence other than saying "Ukraine still has Soviet nuclear technologies and the means of delivery of such weapons."
More than 100 diplomats walked out of the hall in protest as his speech began, underlining Russia's international isolation.
Ukraine's general staff said Russian losses included 5,710 personnel, 29 destroyed and damaged aircraft and 198 tanks, all figures that could not be verified. Russia has given no full account of its battlefield losses.
Moscow announced a ban on foreign companies selling assets to try to halt the flight of Western companies abandoning their Russian ties. Putin also issued a decree banning cash exports of foreign currency from Russia exceeding $10,000 in value.
The rouble hit a record low on Tuesday, threatening the living standards of ordinary Russians. Most effective among the sanctions so far have been those on Russia's central bank that prevent it from using its $630 billion foreign reserve war chest to prop up the rouble.
With energy prices soaring, the US and its allies agreed Tuesday to release oil reserves as buyers avoid Russian suppliers.
The Kremlin accused the EU of hostile behavior, saying weapons supplies to Ukraine were destabilizing and proved that Russia was right in its efforts to demilitarize its neighbor.
But there was support for Ukraine from unexpected quarters.
US technology firm Microsoft said it had provided threat intelligence and defensive suggestions to Ukrainian officials about attacks on a range of targets, and also advised the government about attempted cyberthefts of data.
Google said on Tuesday that it had blocked mobile apps connected to RT and Sputnik from its Play store, in line with an earlier move to remove the Russian state publishers from its news-related features.
A number of tech companies have limited distribution and advertising tools to Russian news outlets in recent days as the European Commission readies a ban on them out of concern that they are spreading misinformation about the war in Ukraine.
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RT Deputy Editor-in-Chief Anna Belkina said in a statement on Tuesday that technology companies that have cut her outlet's distribution have not pointed to any evidence that it has reported falsehoods.
Apple said that RT News and Sputnik News were no longer available for download from its App Store outside Russia.
And European soccer's governing body, UEFA, scrapped sponsorship by the Russian state gas giant Gazprom reported to be worth 40 million euros ($45 million) a season, and UEFA and the global federation FIFA suspended all Russian teams until further notice.
Turkish President Recep Tayyip Erdogan on Tuesday called on Ukraine and Russia to immediately stop fighting and to "contribute to world peace," adding that Ankara was not opposed to NATO enlargement.
NATO member Turkey shares a maritime border with Ukraine and Russia and has good ties with both. Under a 1936 pact, Ankara on Monday said it was closing its Black Sea straits during Russia's invasion of Ukraine, limiting the passage of some Russian ships from the Mediterranean.
Asked about Ukraine's bid for European Union membership at a news conference in Ankara, Erdogan said Turkey, an EU candidate for decades, would support any enlargement of NATO and the EU.
Erdogan called on the bloc to show the "same sensitivity" it showed for Kyiv's membership bid for Turkey's application, and slammed member states for being "not sincere."
"Will you put Turkey on your agenda when someone attacks [us] too?" he asked.