Russian President Vladimir Putin on Wednesday said Moscow was ready to discuss neutral status for its neighbour but would still achieve the goals of its operation, which he said was "going to plan".
But Putin acknowleded that Western sanctions imposed on Russia in response to its actions were hurting.
In Washington, US President Joe Biden called Putin a "war criminal". The United States is not seeing Russia take any actions that would suggest progress in talks between Russian and Ukrainian officials, White House spokeswoman Jen Psaki said.
Earlier, Ukraine's President Volodymyr Zelenskiy said talks between Moscow and Kyiv were becoming "more realistic" and Russia's foreign minister said proposals under discussion were "close to an agreement".
On the 21st day of the conflict, Russian forces kept up their bombardments of besieged cities, including intensified shelling of the capital Kyiv.
The US Embassy in Kyiv said Russian forces had shot dead 10 people waiting in line for bread in Chernihiv, northeast of Kyiv. Footage from Ukraine's state broadcaster showed bodies lying on the street. Ukraine's general prosecutor's office said it had opened an investigation.
Russia denied the attack and said the incident was a hoax.
Emergency service said rescue workers had found the bodies of five people, including three children, during searches of shell-hit residential buildings in Chernihiv.
In the besieged southern port of Mariupol, the city council said Russian forces bombed a theatre where civilians were sheltering. The number of casualties was not known.
Russia's defence ministry denied it had carried out an air strike against the theatre. Reuters could not independently verify the information.
The governor of Zaporizhzhia region said Russian forces had fired artillery at a convoy of evacuees from Mariupol, wounding five people. Ukraine's military said children were among the casualties.
Three people were killed and five wounded after shelling caused a fire at a market in eastern Kharkiv, Ukraine's second city, emergency services said.
Deputy Prime Minister Iryna Vereshchuk said 400 staff and patients were being held hostage at a hospital Russian forces had captured in Mariupol on Tuesday.
Moscow denies targeting civilians.
Kyiv's mayor Vitali Klitschko said Russian shelling caused a fire and damaged private homes and a gas line there on Wednesday evening after early morning barrages.
Russian troops have halted at the gates of the capital after taking heavy losses and failing to seize any major city in a war Western officials say Moscow expected to win within days.
In a speech to the US Congress by video link, Zelenskiy appealed for tougher sanctions on Russia and more weapons to help his country.
He invoked the 1941 attack on Pearl Harbor and quoted Martin Luther King's "I have a dream" speech to call for a no-fly zone over Ukraine.
"In the darkest time for our country, for the whole of Europe, I call on you to do more," said Zelenskiy, who showed video clips of dead and wounded children and blasted buildings.
The White House said Biden had not changed his opposition to a no-fly zone, something military experts say would be equivalent to the United States entering the war against Russia.
But he did offer an additional $US800 million ($A1.1 billion) in security assistance to Ukraine. This included 800 anti-aircraft systems "to make sure that the Ukrainian military can continue to stop the planes and helicopters that have been attacking their people," Biden said.
NATO defence ministers meeting in Brussels also pledged more arms supplies to help Ukraine fight off the Russian invasion.
Talks were due on Wednesday by a video link for a third straight day. Zelenskiy said overnight that the positions already sounded "more realistic".
The Kremlin said negotiators were discussing status for Ukraine similar to that of Austria or Sweden, both members of the European Union that are outside the NATO military alliance.
Ukraine's chief negotiator said Kyiv was still demanding a ceasefire and the withdrawal of Russian troops, with guarantees.
The signs of compromise sent relief through global financial markets.
While Russia has long objected to Ukraine's NATO ambitions, Kyiv and its allies have said Moscow's true aim was to overthrow Ukraine's pro-Western, elected leaders.