Russia's defence ministry said it had captured Kherson on Wednesday but an adviser to Ukrainian President Volodymyr Zelenskiy responded that Ukrainian forces continued to defend the Black Sea port of about 250,000 people.

"We are a people who broke the enemy's plans in a week," Zelenskiy said in a video address.

"These plans had taken years to write - they are mean, with hatred for our country, for our people."

The capture of the strategic southern provincial capital, where the Dnipro River flows into the Black Sea, would be the first significant urban centre to fall since Moscow launched its invasion on February 24.

Russian forces have yet to overthrow the government in Kyiv but thousands are reported to have died or been injured and more than a million people have fled Ukraine amid the biggest attack on a European state since 1945.

Russia's attack has led to a barrage of international sanctions that threaten the global economic recovery from the COVID pandemic, and stoked fears of wider conflict as Western countries send arms to help the Ukrainian military.

Kherson Mayor Igor Kolykhayev said late on Wednesday that Russian troops were in the streets and had entered the council building. He called on civilians to walk through the streets only in daylight and in ones and twos.

"There were armed visitors in the city executive committee today," he said in a statement. "I didn't make any promises to them ... I just asked them not to shoot people."

Russia calls its actions in Ukraine a "special operation" that is not designed to occupy territory but to destroy its neighbour's military capabilities and capture what it regards as dangerous nationalists.

It denies targeting civilians although there have been widespread reports of civilian casualties and the shelling of residential areas.

Bombing in Kharkiv, a city of 1.5 million people, has left its centre a wasteland of ruined buildings and debris.

Russians have shelled the city of Izyum, about 120km southeast of Kharkiv, killing six adults and two children, Ukraine's parliament said.

An explosion also rocked the Kyiv railway station where thousands of women and children were being evacuated. The blast was caused by wreckage from a downed Russian cruise missile, a Ukrainian interior ministry adviser said, and there were no immediate reports of casualties.

An investigation into possible war crimes will immediately be opened by the International Criminal Court, following requests by 39 of the court's member states, an unprecedented number.

A UN resolution reprimanding Moscow was supported by 141 of the assembly's 193 members, a symbolic victory for Ukraine that increases Moscow's international isolation.

"More is at stake even than the conflict in Ukraine itself. This is a threat to the security of Europe and the entire rules-based order," US Secretary of State Antony Blinken said.

Oil and commodity prices spiralled ever higher on Thursday in a grim omen for global inflation.

For Russians, the fallout has included queues outside banks, a plunge in the value of the rouble which threatens their living standards, and an exodus of Western firms who refuse to do business in the country.

Russia's central bank, itself under sanctions, has doubled interest rates to 20% and Fitch downgraded Russia's sovereign credit rating to 'junk' status.

A Ukrainian delegation had left for a second round of talks with Russian officials on a ceasefire after a first round made little progress on Monday, Ukrainian presidential adviser Mykhailo Podolyak told Reuters.

The UN Human Rights Office said it had confirmed the deaths of 227 civilians and 525 injuries during the conflict as of midnight on March 1, mostly caused by "the use of explosive weapons with a wide impact area".

Russian businessman Roman Abramovich said he would sell London's Chelsea Football Club and donate money to help victims of the war in Ukraine.

Australian Associated Press