When Russia seized Crimea in 2014, President Vladimir V. Putin was so worried about Russian casualty figures coming to light that authorities accosted journalists who tried to cover funerals of some of the 400 troops killed during that one-month campaign.

But Moscow may be losing that many soldiers daily in Putin’s latest invasion of Ukraine, American and European officials said. The mounting toll for Russian troops exposes a potential weakness for the Russian President at a time when he is still claiming, publicly, that he is engaged only in a limited military operation in Ukraine’s separatist east.

No one can say with certainty just how many Russian troops have died since last Thursday, when they began what is turning into a long march to Kyiv, the capital. Some Russian units have put down their arms and refused to fight, the Pentagon said Tuesday. Major Ukrainian cities have withstood the onslaught thus far.

American officials had expected the northeastern city of Kharkiv to fall in a day, for example, but Ukrainian troops there have fought back and regained control despite furious rocket fire. The bodies of Russian soldiers have been left in areas surrounding Kharkiv.

Videos and photos on social media show charred remains of tanks and armored vehicles, their crews dead or wounded.

The Russian defence ministry spokesman, Major General Igor Konashenkov, acknowledged on Sunday for the first time that “there are dead and wounded” Russian troops but offered no numbers. He insisted Ukrainian losses were “many times” higher. Ukraine has said its forces have killed more than 5,300 Russian troops.

Neither side’s claims have been independently verified, and Biden administration officials have refused to discuss casualty figures publicly. But one American official put the Russian losses as of Monday at 2,000, an estimate with which two European officials concurred.

Senior Pentagon officials told lawmakers in closed briefings on Monday that Russian and Ukrainian military deaths appeared to be the same, at around 1,500 on each side in the first five days, congressional officials said. But they cautioned that the figures — based on satellite imagery, communication intercepts, social media and on-the-ground media reports — were estimates.

For a comparison, nearly 2,500 American troops were killed in Afghanistan over 20 years of war.

For Putin, the rising death toll could damage any remaining domestic support for his Ukrainian endeavours. Russian memories are long — and mothers of soldiers, in particular, American officials say, could easily hark back to the 15,000 troops killed when the Soviet Union invaded and occupied Afghanistan, or the thousands killed in Chechnya.

Russia has deployed field hospitals near the front lines, say military analysts, who have also monitored ambulances driving back and forth from Russian units to hospitals in Belarus, Moscow’s ally.

“Given the many reports of over 4,000 Russians killed in action, it is clear that something dramatic is happening,” said Admiral James G. Stavridis, who was Nato’s supreme allied commander before his retirement. “If Russian losses are this significant, Vladimir Putin is going to have some difficult explaining to do on his home front.”

New York Times News Service