The number of Russian troops killed and wounded in Ukraine is approaching 200,000, a stark symbol of just how badly President Vladimir V. Putin’s invasion has gone, according to American and other western officials.

While the officials caution that casualties are notoriously difficult to estimate, particularly because Moscow is believed to routinely undercount its war dead and injured, they say the slaughter from fighting in and around the eastern Ukrainian city of Bakhmut and Soledar has ballooned what was already a heavy toll.

With Moscow desperate for a major battlefield victory and viewing Bakhmut as the key to seizing the entire eastern Donbas area, the Russian military has sent poorly trained recruits and former convicts to the front lines, straight into the path of Ukrainian shelling and machine guns.

The result, American officials say, has been hundreds of troops killed or injured a day. Russia analysts say that the loss of life is unlikely to be a deterrent to Putin’s war aims. He has no political opposition at home and has framed the war as the kind of struggle the country faced in World War II, when more than 8 million Soviet troops died.

US officials have said that they believe that Putin can sustain hundreds of thousands of casualties in Ukraine, although higher numbers could cut into his political support. Ukraine’s casualty figures are also difficult to ascertain, given Kyiv’s reluctance to disclose its own wartime losses. But in Bakhmut, hundreds of Ukrainian troops have been wounded and killed daily at times as well, officials said.

Better trained infantry formations are kept in reserve to safeguard them, while lesser prepared troops, such as those in the territorial defence units, are kept on the front line and bear the brunt of shelling.

The last public Biden administration estimate of casualties came last November, when General Mark A.Milley, the chairman of the Joint Chiefs of Staff, said that more than 100,000 troops on each side had been killed and wounded since the war began. At the time, officials said privately that the numbers were closer to 120,000.

“I would say it’s significantly well over 100,000 now,” General Milley said at a news conference last month in Germany, adding that the Russian toll included “regular military, and also their mercenaries in the Wagner Group”.

At two meetings last month between senior military and defence officials fromNato and partner countries, officials said the fighting in the Donbas had turned into, as one of them put it, a meatgrinder.