TOP WRAP 2-Russian troops in strategic Black Sea port city of Kherson, mayor says

* Eastern city of Kharkiv suffers further heavy bombardment

* Moscow says it has seized Kherson, mayor says troops in streets

* UN votes overwhelmingly to censure Russia's invasion

* Unprecedented number of nations seek war crimes probe

KYIV/KHARKIV, Ukraine, March 3 (Reuters) - Russian troops are in the southern Ukrainian city of Kherson and forced their way into the council building, the mayor said after a day of conflicting claims over whether Moscow had made the first major gain of a city in its eight-day-long invasion.

The incursion has yet to overthrow the government in Kyiv but thousands are reported to have died or been injured and more than 870,000 have fled Ukraine.

The biggest attack on a European state since 1945 has also caused ructions in a global economy still recovering from the COVID pandemic, led to a barrage of sanctions against Russia and stoked fears of wider conflict in the West.

For Russians, the fallout has included queues outside banks, a plunge in the value of the rouble, and an exodus of firms while Ukrainians are counting the cost of bombings despite fresh global support, including at the United Nations.

The Black Sea port of Kherson, a southern provincial capital of around 250,000 people, is strategically placed where the Dnipro River flows into the Black Sea and would be the first significant city to fall into Moscow's hands.

Russia's defence ministry said on Wednesday morning it had captured Kherson but several hours later an adviser to President Volodymyr Zelenskiy responded the Ukrainian side was continuing to defend the location.

Late on Wednesday, Mayor Igor Kolykhayev said Russian troops were in the streets.

"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."

He called on civilians to walk through the streets only in daylight and in ones and twos.

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.

In other incidents, 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, some 120 km south east of Kharkiv, killing six adults and two children, Ukraine's parliament said.

An explosion also rocked the Kyiv railway station during the night, where thousands of women and children were being evacuated.