Thousands of civilians are believed to have died. Estimates of Russian military casualties vary widely, but even conservative figures by Western officials are in the low thousands.
On Monday, Russia's pro-Kremlin Komsomolskaya Pravda newspaper, citing the Defense Ministry, reported that almost 10,000 Russian soldiers had been killed. The report was quickly removed, and the newspaper blamed hackers. The Kremlin refused to comment. The Western official said the figure is "a reasonable estimate."
Facing unexpectedly stiff resistance that has left the bulk of Moscow's ground forces miles from the centre of Kyiv, Putin's troops are increasingly concentrating their air power and artillery on Ukraine's cities and civilians.
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Talks to end the fighting have continued by video. Ukrainian President Volodymyr Zelenskyy has said he would be prepared to consider waiving any bid by Ukraine to join NATO "a key Russian demand" in exchange for a cease-fire, the withdrawal of Russian troops and a guarantee of Ukraine's security.
UN Secretary-General Antonio Guterres said he saw progress in the talks. "From my outreach with various actors, elements of diplomatic progress are coming into view on several key issues," and the gains are enough to end hostilities now, he said. He gave no details.
The Western official, though, said that there were no signs Moscow was ready to compromise.