More than 11,000 Russian troops have been killed since Moscow launched an invasion of Ukraine on Feb. 24, the Ukrainian armed forces' general staff said on Sunday.
A day earlier, it put Russian casualties at over 10,000. It did not report Ukrainian casualties.
On Sunday, the fight stopped about 200,000 people from evacuating the besieged Ukrainian city of Mariupol for the second day in a row.
Meanwhile, Russian President Vladimir Putin vowed to press ahead with his invasion unless Kyiv surrendered.
Most people trapped in the port city are sleeping underground to escape more than six days of near-constant shelling by encircling Russian forces that have cut off food, water, power and heating supplies, according to the Ukrainian authorities.
In a phone call with Turkish President Tayyip Erdogan, Putin said he was ready for dialogue to end the fighting but that any attempt to draw out talks would fail, according to the Kremlin.
The suspension of what Moscow describes as a special operation, "is only possible if Kyiv stops military operations and carries out well-known Russian demands," the Kremlin said in a readout of the Putin-Erdogan call.
The civilian death toll from hostilities across Ukraine since Moscow launched its invasion on Feb. 24 stood at 364, including more than 20 children, the United Nations said on Sunday, adding that hundreds more were injured.
The U.N. High Commissioner for Human Rights said most civilian casualties were caused by the use of "explosive weapons with a wide impact area, including shelling from heavy artillery and multi-launch rocket systems, and missile and airstrikes."
Russia has launched about 600 missiles so far, according to a senior U.S. defence official.
The general staff of Ukraine's armed forces said the Russians were "beginning to accumulate resources for the storming of Kyiv".
Moscow has repeatedly denied attacking civilian areas.
In Irpin, a town some 25 km (16 miles) northwest of the capital Kyiv, men, women and children trying to escape heavy fighting in the area were forced to take cover when missiles struck nearby, according to Reuters witnesses.
Soldiers and fellow residents helped the elderly hurry to a bus filled with frightened people, some cowering as they waited to be driven to safety.
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The invasion has drawn widespread condemnation around the world, sent more than 1.5 million Ukrainians fleeing from the country, and triggered sweeping Western sanctions against Russia aimed at crippling its economy.
The Biden administration said on Sunday it was exploring banning imports of Russian oil, despite concerns the move would drive prices even higher.
Oil prices have soared to their highest levels since 2008 and jumped 10% in early Asian trade on Monday. Russia provides 7% of the global supply.
"War is madness, please stop," Pope Francis said in his weekly address to crowds in St Peter's Square, adding "rivers of blood and tears" were flowing in Ukraine's war.
Russian media said Putin also spoke by phone for almost two hours with French President Emmanuel Macron. Macron told Putin he was concerned about a possible amphibious attack on Ukraine's historic port city of Odessa, Macron's office said.
The United States does not believe such an attack is imminent, the senior U.S. defense official said, speaking on condition of anonymity.