The number of Ukrainian refugees was expected to reach 1.5 million on Sunday as Russia continued its attack 11 days after invading Ukraine and Kyiv pressed for further Western action, including more sanctions and weapons, Reuters reports.
Moscow and Kyiv traded blame over a failed ceasefire plan that would have let civilians flee Mariupol and Volnovakha, two southern cities besieged by Russian forces.
Another round of talks was tentatively planned for Monday as Ukrainians who could escape spilled into neighboring Poland, Romania, Slovakia and elsewhere.
In a televised address on Saturday night, Ukraine's President Volodymyr Zelenskiy called on people in areas occupied by Russian troops to go on the offensive and fight.
"We must go outside and drive this evil out of our cities," he said, vowing to rebuild his nation. "My confidence in this is reinforced by the energy of our resistance, our protest."
Russian President Vladimir Putin earlier reiterated that he wanted a neutral Ukraine that had been "demilitarised" and "denazified," and likened Western sanctions "to a declaration of war," adding: "Thank God it has not come to that."
Ukraine and Western countries have decried Putin's reasons as a baseless pretext for the invasion he launched on February 24 and have imposed sweeping sanctions aimed at isolating Moscow and crippling its economy.
Ukraine's Foreign Minister Dmytro Kuleba, after meeting with US Secretary of State Antony Blinken at the Ukraine-Poland border, said he expected new sanctions and weapons for Ukraine in coming days.
The United States has said it would give Ukraine more weapons and has repeatedly warned it could escalate sanctions, with President Joe Biden seeking $10 billion in emergency funding to respond to the crisis.
Washington is working with Poland as Warsaw considers whether to provide fighter jets to Ukraine, a White House spokesperson said late on Saturday, adding that the United States could replenish Poland's supply of jets if they did, although challenges remain given the contested airspace.
Zelenskiy had asked for help securing aircraft from European allies in a video call with US lawmakers earlier on Saturday. He also called again for more lethal aid, a ban on Russian oil, a no-fly zone and an end to Visa Inc and MasterCard Inc privileges in Russia, US media reported.
Biden spoke with Zelenskiy for about 30 minutes on Saturday evening in Washington as Sunday broke in Ukraine, the White House said. They discussed security, financial support for Ukraine and the continuation of sanctions against Russia, Zelenskiy wrote on Twitter.
NATO, which Ukraine wants to join, has resisted Zelenskiy's appeals to impose a no-fly zone over his country, saying it would escalate the conflict outside Ukraine.
Seeking to mediate, Israeli Prime Minister Naftali Bennett met with Putin at the Kremlin on Saturday and later spoke to Zelenskiy, Bennett's spokesperson said.
"We continue dialogue," Zelenskiy tweeted after the call.