Earlier, Zelenskyy underlined the importance of defending Bakhmut, saying its fall could allow Moscow to rally international support for a deal that might require Kyiv to make unacceptable compromises.
The Ukrainian leader arrived on a French government plane. He is also due to attend the G7 leaders' summit in the Japanese city of Hiroshima this weekend, although this could take place virtually.
The delegation is harshly criticized for meeting with Russian officials while the Kremlin is waging a war against Ukraine.
"The enemy's targets are the places where we live. Their targets are our lives and the lives of our children," Governor Oleksandr Prokudin said
"Attempts to disown this, both in Kyiv and in Washington, are, of course, absolutely ridiculous. We know very well that decisions about such actions... are made not in Kyiv but in Washington," Putin's spokesman Dmitry Peskov said.
Air raid sirens sound around Kyiv in the first attack against the capital in nearly two months.
The Russian president travels to the Crimean peninsula, among others, to mark the 9-year anniversary of its annexation. The chances of Putin facing trial at the ICC are highly unlikely as Moscow does not recognize the court’s jurisdiction or extradite its nationals.
The court also issued a warrant for the arrest of Maria Lvova-Belova, the commissioner for Children’s Rights in the Office of the President of the Russian Federation over the abduction of Ukrainian orphans in October.
Among potential crimes, the report cited "systematic and widespread use of torture", as well as "repeated attacks targeting Ukrainian infrastructure".
President Volodymyr Zelenskyy described the barrage that came while many people slept as an attempt by Moscow “to intimidate Ukrainians again.”