Ukraine's second biggest city, Kharkiv, has suffered heavy bombardment as Russia's week-long invasion was denounced by the United Nations in a historic vote and dozens of countries referred Moscow to be probed for potential war crimes.
Ukrainians have denied a claim by Russia that its forces had taken the Black Sea port of Kherson.
A US official has said that control of Kherson remained contested and that Russian forces appeared to be getting more aggressive in targeting infrastructure inside Kyiv as its advances slow in the face of fierce Ukrainian resistance.
The invasion has yet to achieve Russian President Vladimir Putin's aim of overthrowing Ukraine's government but it has sent more than 870,000 people fleeing to neighbouring countries and jolted the global economy as governments and companies line up to isolate Moscow.
The United Nations General Assembly voted overwhelmingly to deplore the invasion "in the strongest terms". It demanded that Russia withdraw its forces in a resolution backed by 141 of the assembly's 193 members.
While General Assembly resolutions are non-binding, they carry political weight, with today's vote representing a symbolic victory for Ukraine and increasing Moscow's international isolation.
After nearly a week since the invasion began, more than 2,000 civilians have been killed according to the Ukrainian emergency service. Hospitals, kindergartens and homes have also been destroyed.
Meanwhile, Russia's defence ministry has said that 498 Russian soldiers had died in Ukraine and another 1,597 had been wounded since the beginning of Moscow's military operation there, Russia's RIA news agency reported. It was the first time that Moscow had put a figure on its casualties.
The Ukrainian city of Kharkiv has been hit by further Russian shelling, amid reports that Russian airborne troops have landed in the city near the Russian border | Read more: https://t.co/swet6d9U9g pic.twitter.com/SlBH7ddllI
— RTÉ News (@rtenews) March 2, 2022
French President Emmanuel Macron hailed the courage of Ukrainians faced with a war he said was Mr Putin's responsibility alone.
"The days ahead are likely to be increasingly difficult," Mr Macron said in a televised national address.
The UN Human Rights Office said it had confirmed the deaths of 227 civilians and 525 injuries during the conflict in Ukraine as of midnight on 1 March, mostly caused by "the use of explosive weapons with a wide impact area". It cautioned that the real toll would be much higher due to reporting delays.
After failing to swiftly take major cities and to subdue Ukraine's military, US officials have said for days that they believe Russia will instead seek to encircle cities, cutting off supply and escape routes, then attacking with a combined force of armour, ground troops and engineers.
The invasion has sent more than 870,000 people fleeing over Ukraine's borders and retaliatory sanctions have shaken the world economy, with surging oil prices exacerbating fears of inflation.

The most intensive bombardment has struck Kharkiv, a city of 1.5 million people in the east, turning the centre into a bombed-out wasteland of ruined buildings and debris.
At least 25 people have been killed by shelling and airstrikes in Kharkiv in the past 24 hours, authorities said.
After an air strike this morning, the roof of a police building in central Kharkiv collapsed as it was engulfed in flames.
Moscow denies targeting civilians and says it aims to disarm Ukraine, a country of 44 million people, in a "special military operation".
Apple, Exxon, Boeing and other firms joined an exodus of international companies from Russian markets that has left Moscow financially and diplomatically isolated.
Both the European Union and the United States also imposed new sanctions on Belarus for its supporting role in the invasion.
Amid calls for him to face sanctions, Russian businessman Roman Abramovich said he would sell London's Chelsea Football Club and donate money from the sale to help victims of the war.
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Hopes for a diplomatic way out of the crisis continued to flicker. Ukrainian presidential adviser Mykhailo Podolyak told Reuters that 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.
President Volodymyr Zelenskiy has said Russia must stop bombing if it wants to negotiate.
"He thought he could roll into Ukraine and the world would roll over. Instead, he met a wall of strength he could never have anticipated or imagined: he met Ukrainian people," US President Joe Biden said yesterday in his annual State of the Union address.
US lawmakers stood, applauded and roared, many waving Ukrainian flags and wearing its blue and yellow colours.
'We're coming for your ill-begotten gains,' US President Joe Biden warned Russian oligarchs as he pledged 'support to the Ukrainians in their fight for freedom' during his State of the Union address | Read more: https://t.co/ob4kjw0HsN pic.twitter.com/Mx58U9s00F
— RTÉ News (@rtenews) March 2, 2022
Also in the south, Russia was bombarding the port of Mariupol, which it said it has surrounded in a ring around the entire Sea of Azov. The besieged city's mayor said Mariupol had suffered mass casualties after a night of intense strikes. He gave no full casualty figure, but said it was impossible to evacuate the wounded and that water supplies were cut.
"The enemy occupying forces of the Russian Federation have done everything to block the exit of civilians from the city of half a million people," mayor Vadym Boichenko said in a live broadcast on Ukrainian TV.
Lavrov requests list of weapons

Russian Foreign Minister Sergei Lavrov has said that Moscow remained committed to the demilitarisation of Ukraine and there should be a list of specified weapons that could never be deployed on Ukrainian territory.
"Specific types of strike weapons must be identified which will never be deployed in Ukraine and will not be created," Mr Lavrov said in an interview with Al Jazeera, the text of which was published on his ministry's website.
Mr Lavrov said Russia recognised Mr Zelensky as Ukraine's leader and welcomed as a "positive step" the fact that Zelensky wanted to receive security guarantees.
"Our negotiators are ready for the second round of discussing these guarantees with Ukrainian representatives," he said.
Meanwhile, Poland, the Czech Republic, Bulgaria, Slovakia and Romania will quit two Soviet-era international banks which count Russia as their largest shareholder, their finance ministries said today.
The move follows the announcement by the Czech Republic on Friday, which said it would quit the International Bank for Economic Cooperation (IBEC) and the International Investment Bank (IIB) and called on other EU member states to do likewise.

Russia's main advance on the capital - a huge armoured column, stretching for miles along the road to Kyiv - has been largely frozen in place for days, Western governments say.
The Kremlin's decision to launch war - after months of denying such plans - has shocked Russians accustomed to viewing Putin, their ruler of 22 years, as a methodical strategist.
Russia's rouble currency plunged to a new record low today, a slide that will hit Russians' living standards, and the stock market remained closed. The central bank, itself under sanctions, has doubled interest rates to 20%.
In an echo of the post-Soviet economic collapse of the1990s, Russians have queued at banks to salvage their savings.