Russia's defence ministry on Thursday said a fire on the Moskva missile cruiser caused ammunition to blow up, Interfax news agency reported.
It did not say what caused the fire but Maksym Marchenko, the Ukrainian governor of the region around the Black Sea port of Odesa, said the Moskva had been hit by two Ukrainian-made Neptune anti-ship cruise missiles.
Reuters was unable to verify either side's claims.
The Moskva is the second major ship known to have suffered serious damage since the start of the war. In March, Ukraine said it had destroyed a landing support ship, the Orsk, on the smaller Sea of Azov.
Russia's navy has launched cruise missiles into Ukraine and its activities in the Black Sea are crucial to supporting land operations in the south of the country, where it is battling to seize full control of the port of Mariupol.
Russia said 1026 soldiers from Ukraine's 36th Marine Brigade, including 162 officers, had surrendered in Mariupol and that the city was fully under its control. Ukraine's defence ministry spokesman said he had no information about a surrender.
Capturing the Azovstal industrial district where the marines have been holed up would give Russia control of Ukraine's main Sea of Azov port, reinforce a southern land corridor and expand its occupation of the country's east.
"Russian forces are increasing their activities on the southern and eastern fronts, attempting to avenge their defeats," President Volodymyr Zelenskiy said in a Wednesday night video address.
Reuters journalists accompanying Russian-backed separatists saw flames billowing from the Azovstal area on Tuesday, a day after Ukraine's 36th Marine Brigade said its troops had run out of ammunition.
The United States said on Wednesday it would send an extra $US800 million ($A1 billion) worth of military hardware to Ukraine including artillery, armoured personnel carriers and helicopters. France and Germany also pledged more.
Senior US officials are weighing whether to send a top cabinet member such as Secretary of State Antony Blinken and Defense Secretary Austin Lloyd to Kyiv in a show of solidarity, a source familiar with the situation said.
Russia will view US and NATO vehicles transporting weapons on Ukrainian territory as legitimate military targets, Deputy Foreign Minister Sergei Ryabkov told the TASS news agency.
Ukrainian Deputy Prime Minister Iryna Vereshchuk said nine humanitarian corridors had been agreed to be opened on Thursday to evacuate civilians, including by private car from the besieged city of Mariupol.
Other evacuation routes are from Berdiansk, Tokmak and Enerhodar, and ones in the eastern Luhansk region will operate if occupying Russian forces stop shelling, Vereshchuk added in a statement.
Ukraine says tens of thousands of people are believed to have been killed in Mariupol and accuses Russia of blocking aid convoys to civilians marooned there.
Moscow has blamed Ukraine for civilian deaths and accused Kyiv of denigrating Russian armed forces.
The Kremlin denounced President Joe Biden's description of Moscow's actions in Ukraine as amounting to genocide, with spokesman Dmitry Peskov saying this was unacceptable coming from the leader of a country he said had committed crimes of its own.
An initial report by a mission of experts set up by the Organization for Security and Cooperation in Europe documents a "catalogue of inhumanity" by Russian troops in Ukraine, according to the US ambassador to the OSCE.
Russia has denied targeting civilians.
The Kyiv district police chief said 720 bodies had been found in the region around the capital from where Russian forces had retreated, with more than 200 people missing.
Britain announced new financial measures on separatists, and Australia imposed targeted financial sanctions on 14 Russian state-owned enterprises on Thursday. Moscow and Washington have exchanged tit-for-tat sanctions on individual lawmakers.
