A Russian delegate to talks with Ukraine was quoted on Sunday as saying they had made significant progress and it was possible the delegations could soon reach draft agreements, although he did not say what these would cover.
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Russia's RIA news agency quoted Leonid Slutsky as comparing the state of the talks now with the situation when they first started, and saying there was "substantial progress."
His comments came on day 18 of the war which began when Russian forces invaded Ukraine on Feb. 24 in what the Kremlin terms a special military operation.
"According to my personal expectations, this progress may grow in the coming days into a joint position of both delegations, into documents for signing," Slutsky said.
Ukrainian negotiator and presidential adviser Mykhailo Podolyak on Sunday said he thought progress could be made at talks with Russia in the coming days as the Russian side had become more constructive.
"We will not concede in principle on any positions. Russia now understands this. Russia is already beginning to talk constructively. I think that we will achieve some results literally in a matter of days," Podolyak said in a video posted online.
Meanwhile, Ukraine's president says nearly 125,000 civilians have been evacuated through safe-passage corridors so far, and a convoy with humanitarian aid is headed to the besieged city of Mariupol.
"We have already evacuated almost 125,000 people to the safe territory through humanitarian corridors," Volodymyr Zelenskyy said in a video address released Sunday. "The main task today is Mariupol. Our convoy with humanitarian aid is two hours away from Mariupol. Only 80 km (left)."
"We're doing everything to counter occupiers who are even blocking Orthodox priests accompanying this aid, food, water and medicine. There are 100 tons of the most necessary things that Ukraine sent to its citizens," Zelenskyy said.
Waves of Russian missiles pounded a military training base close to Ukraine's western border with NATO member Poland on Sunday, killing 35 people. The strike followed Russian threats to target foreign weapon shipments that are helping Ukrainian fighters defend their country against Russia's grinding invasion.

More than 30 Russian cruise missiles targeted the sprawling training facility that is less than 25 kilometers (15 miles) from the closest border point with Poland, according to the governor of Ukraine's western Lviv region. Poland is a key location for routing Western military aid to Ukraine.
Since Russia invaded Ukraine, Lviv had largely been spared the scale of destruction unfolding further east and become a destination for residents escaping bombarded cities and for many of the nearly 2.6 million refugees who have fled the country.
The training center in Yavoriv appears to be the most westward target struck so far in the 18-day invasion. The facility, also known as the International Peacekeeping and Security Center, has long been used to train Ukrainian military personnel, often with instructors from the United States and other NATO countries.
The office of Ukraine's Prosecutor General says a total of 85 children have been killed since the start of the Russian offensive in Ukraine.

More than 100 more have been wounded, the office said. Officials also said that bombings and shelling have damaged 369 educational facilities in the country, 57 of which have been completely destroyed.
Foreign Minister Yair Lapid met with Romanian foreign Minister Bogdan Aurescu on Sunday during a visit to Romania to discuss the Ukraine war.
At the end of the meeting, Lapid said, "Israel, like Romania, condemns the Russian invasion of Ukraine. It is unjustified, and we call on Russia to stop the shelling and the assaults and solve the problems [in talks] around the negotiating table."
Lapid also said Israel would do everything it could to help broker a peaceful solution. "We are working with our ally, the US, and the European partners to try and end this violent tragedy as quickly as possible," he said.
Lapid that that following his working meeting with Aurescu, the two would meet with the Romanian prime minister to discuss the Ukraine crisis and how to handle refugees from Ukraine. Lapid also said he planned to visit a refugee center set up by the Jewish Agency for Israel in Bucharest.
Ukraine is working with Israel and Turkey as mediators to finalize a location and framework for peace negotiations with Russia, Ukrainian presidential adviser and negotiator Mykhailo Podolyak said on Sunday.
"When it is worked out, there will be a meeting. I think it won't take long for us to get there," he said on national television.
As millions of women and children flee across Ukraine's borders in the face of Russian aggression, concerns are growing over how to protect the most vulnerable refugees from being targeted by human traffickers or becoming victims of other forms of exploitation.
One man was detained in Poland suspected of raping a 19-year-old refugee he'd lured with offers of shelter after she fled war-torn Ukraine. Another was overheard promising work and a room to a 16-year-old girl before authorities intervened.
Another case inside a refugee camp at Poland's Medyka border, raised suspicions when a man was offering help only to women and children. When questioned by police, he changed his story.
As millions of women and children flee across Ukraine's borders in the face of Russian aggression, concerns are growing over how to protect the most vulnerable refugees from being targeted by human traffickers or becoming victims of other forms of exploitation.
"Obviously all the refugees are women and children," said Joung-ah Ghedini-Williams, the UNHCR's head of global communications, who has visited borders in Romania, Poland and Moldova.
The UN refugee agency says more than 2.5 million people, including more than a million children, have already fled war-torn Ukraine in what has become an unprecedented humanitarian crisis in Europe and its fastest exodus since World War II.
Tamara Barnett, director of operations at the Human Trafficking Foundation, a U.K.-based charity which grew out of the All Party Parliamentary Group on Human Trafficking, said that such a rapid, mass displacement of people could be a "recipe for disaster."
"When you've suddenly got a huge cohort of really vulnerable people who need money and assistance immediately," she said, "it's sort of a breeding ground for exploitative situations and sexual exploitation. When I saw all these volunteers offering their houses … that flagged a worry in my head."
Meanwhile, in Russia, Russian President Vladimir Putin said Thursday that if foreign companies shut down production in Russia, he favored a plan to "bring in outside management and then transfer these companies to those who want to work."
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A draft law could allow Russian courts to appoint external administrators for companies that cease operations and are at least 25% foreign-owned. If the owners refuse to resume operations or to sell, the company's shares could be auctioned off, the ruling United Russia party has said, calling it "the first step toward nationalization."
Chris Weafer of Macro-Advisory, a consultancy specializing in Russia, said the Russian government "is adopting a carrot-and-stick approach to foreign business," with talk of nationalization balanced out with government help for those who stay. A key reason, Weafer said, is the Kremlin's desire to avoid mass unemployment.
"When it comes to social pressures or potential public backlash, what they understand, I guess, is that people will not take to the streets because they cannot buy a Big Mac," Weafer said. "But they might take to the streets if they have no job and no income."
White House press secretary Jen Psaki criticized "any lawless decision by Russia to seize the assets of these companies," saying that it "will ultimately result in even more economic pain for Russia."
"It will compound the clear message to the global business community that Russia is not a safe place to invest and do business," she said in a tweet, adding that "Russia may also invite legal claims from companies whose property is seized."
The war in Ukraine is also putting the global food supply at risk, with poorer countries in northern Africa, Asia and the Middle East that depend heavily on wheat imports risk suffering significant food insecurity and the conflict poised to drive up already soaring food prices in much of the world, the UN food agency warned Friday.
Ukraine and Russia, which is under heavy economic sanctions for invading its neighbor two weeks ago, account for one-third of global grain exports.
With the conflict's intensity and duration uncertain, "the likely disruptions to agricultural activities of these two major exporters of staple commodities could seriously escalate food insecurity globally, when international food and input prices are already high and vulnerable," said Qu Dongyu, director-general of the Rome-based Food and Agriculture Organization.
The UN agency, known as FAO, also noted that Russia is the lead producer of fertilizer, and a key fertilizer component – urea – has has jumped more than threefold in price in the last 12 months.
There's also the uncertainty over whether Ukraine's wheat ready in June can be harvested as "massive population displacement has reduced the number of agricultural laborers and workers. Accessing agricultural fields would be difficult,″ Qu noted.
Ukraine's ports on the Black Sea are shuttered, and its government this week banned the export of wheat, oats, millet, buckwheat and some other food products to prevent a crisis in its own country.
The ban does not apply to its major global exports of corn and sunflower oil. It and Russia together supply 52% of the world's sunflower oil exports. They also account for 19% of the world's barley supply, 14% of wheat and 4% of corn.