Explosions were heard in Kyiv and the western city of Lviv early on Saturday and the mayor of the Ukrainian capital said rescuers and medics were working at the site of a blast on the outskirts of the city.
There were no immediate details of casualties or damage.
President Volodymyr Zelenskiy said about 2,500 to 3,000 Ukrainian troops have been killed in seven weeks of war with Russia and about 10,000 injured, but there was no count of civilian casualties.
He told CNN on Friday 19,000 to 20,000 Russian soldiers had been killed in the war. Moscow said last month that 1,351 Russian soldiers had been killed and 3,825 wounded.
Reuters could not independently verify either side's numbers.
Russia pledged on Friday to launch more strikes on Kyiv and said it had used cruise missiles to the Vizar factory on the edge of Kyiv, which it said made and repaired missiles, including anti-ship missiles.
The attack followed Thursday's sinking of the Moskva, the flagship of Moscow's Black Sea fleet.
Ukraine said one of its missiles had caused the Moskva to sink, a powerful symbol of its resistance to a better-armed foe. Moscow said the ship sank while being towed in stormy seas after a fire caused by an explosion of ammunition and that more than 500 sailors were evacuated.
The United States believes the Moskva was hit by two Ukrainian missiles and that there were Russian casualties, although numbers were unclear, a senior U.S. official said.
None of the assessments could be independently verified.
Ukraine's military said on Saturday the presence of Russian warships in the Black Sea, armed with sea-launched missiles, suggests that an increased possibility that Russia would use them to strike Ukraine’s defence industry and logistics infrastructure.
It said also that Russia's navy was active in the Sea of Azov to block the port of Mariupol, where ground fighting has intensified as Ukraine said it was trying to break Russia's siege.
Home to 400,000 people before Russia's invasion, Mariupol has been reduced to rubble. Thousands of civilians have died and tens of thousands remain trapped.
"The situation in Mariupol is difficult and hard. Fighting is happening right now. The Russian army is constantly calling on additional units to storm the city," defence ministry spokesperson Oleksandr Motuzyanyk told a briefing. He said the Russians have not completely captured it.
Zelenskiy said the military situation in the south and east was "still very difficult," while praising the work of his armed forces.
"The successes of our military on the battlefield are really significant, historically significant. But they are still not enough to clean our land of the occupiers. We will beat them some more," he said in a late-night video address, calling again for allies to send heavier weapons and for an international embargo on Russian oil.
Zelenskiy has appealed to U.S. President Joe Biden for the United States to designate Russia a "state sponsor of terrorism," joining North Korea, Cuba, Iran and Syria, the Washington Post reported, citing people familiar with their conversation.
A White House spokesperson responded by saying, "We will continue to consider all options to increase the pressure on Putin."
Ukrainian Prime Minister Denys Shmyhal and top finance officials will attend International Monetary Fund and World Bank meetings in Washington next week, sources told Reuters.
It will be the first chance for key Ukrainian officials to meet in person with financial officials from advanced economies since Russia's invasion of Ukraine on Feb. 24.
Holding out in Mariupol
If Moscow captures Mariupol, it would be the first big city to fall.
Russia's defence ministry said it had captured the city's Illich steel works. The report could not be confirmed. Ukrainian defenders are mainly believed to be holding out in Azovstal, another huge steel works.
Both plants are owned by Metinvest, the empire of Ukraine's richest businessman and backbone of Ukraine's industrial east - which told Reuters on Friday it would never let its enterprises operate under Russian occupation.
Moscow has used its naval power to blockade Ukrainian ports and threaten a potential amphibious landing along the coast. Without the Moskva, the largest warship sunk during conflict since Argentina's General Belgrano in the 1982 Falklands war, its ability to menace Ukraine from the sea could be crippled.
Russia initially described its aims in Ukraine as "a special military operation" to disarm its neighbour and defeat nationalists there.
After its invasion force was driven from the outskirts of Kyiv this month, Moscow has said its main war aim is to capture the Donbas, the eastern region partly held by Russian-backed separatists since 2014.
Kyiv and its Western allies say those are bogus justifications for an unprovoked war of aggression that has driven a quarter of Ukraine's 44 million people from their homes and led to the deaths of thousands.