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WASHINGTON — In 36 days of fighting on Iwo Jima during World War II, nearly 7,000 Marines were killed. Now, 20 days after President Vladimir V. Putin of Russia invaded Ukraine, his military has already lost more soldiers, according to American intelligence estimates.

The conservative side of the estimate, at more than 7,000 Russian troop deaths, is greater than the number of American troops killed over 20 years in Iraq and Afghanistan combined.

It is a staggering number amassed in just three weeks of fighting, American officials say, with implications for the combat effectiveness of Russian units, including soldiers in tank formations. Pentagon officials say a 10 percent casualty rate, including dead and wounded, for a single unit renders it unable to carry out combat-related tasks.

With more than 150,000 Russian troops now involved in the war in Ukraine, Russian casualties, when including the estimated 14,000 to 21,000 injured, are near that level. And the Russian military has also lost at least three generals in the fight, according to Ukrainian, NATO and Russian officials.

Pentagon officials say that a high, and rising, number of war dead can destroy the will to continue fighting. The result, they say, has shown up in intelligence reports that senior officials in the Biden administration read every day: One recent report focused on low morale among Russian troops and described soldiers just parking their vehicles and walking off into the woods.

The American officials, who spoke on the condition of anonymity to discuss operational matters, caution that their numbers of Russian troop deaths are inexact, compiled through analysis of the news media, Ukrainian figures (which tend to be high, with the latest at 13,500), Russian figures (which tend to be low, with the latest at 498), satellite imagery and careful perusal of video images of Russian tanks and troops that come under fire.

American military and intelligence officials know, for instance, how many troops are usually in a tank, and can extrapolate from that the number of casualties when an armored vehicle is hit by, say, a Javelin anti-tank missile.

The high rate of casualties goes far to explain why Russia’s much-vaunted force has remained largely stalled outside of Kyiv, Ukraine’s capital.

“Losses like this affect morale and unit cohesion, especially since these soldiers don’t understand why they’re fighting,” said Evelyn Farkas, the top Pentagon official for Russia and Ukraine during the Obama administration. “Your overall situational awareness decreases. Someone’s got to drive, someone’s got to shoot.”

But, she added, “that’s just the land forces.” With Russian ground forces in disarray, Mr. Putin has increasingly looked to the skies to attack Ukrainian cities, residential buildings, hospitals and even schools. That aerial bombardment, officials say, has helped camouflage the Russian military’s poor performance on the ground. President Volodymyr Zelensky of Ukraine said this week that an estimated 1,300 Ukrainian soldiers had been killed in the war.

Signs of Russia’s challenges abound. Late last week, Russian news sources reported that Mr. Putin had put two of his top intelligence officials under house arrest. The officials, who run the Fifth Service of Russia’s main intelligence service, the FSB, were interrogated for providing poor intelligence ahead of the invasion, according to Andrei Soldatov, a Russian security services expert.

“They were in charge of providing political intelligence and cultivating networks of support in Ukraine,” Mr. Soldatov said in an interview. “They told Putin what he wanted to hear” about how the invasion would progress.

Russians themselves may be hearing only what Mr. Putin wants them to hear about his “operation” in Ukraine, which he refuses to call a war or an invasion. Since it began, he has exerted iron control over the news outlets in Russia; state media is not publicizing most casualties, and has minimized the destruction.

But some Russians have access to virtual private networks (VPNs) and are able to get news from the West.

“I don’t believe he can wall off, indefinitely, Russians from the truth,” William J. Burns, the C.I.A. director, told the Senate last Thursday. “Especially as realities began to puncture that bubble, the realities of killed and wounded coming home, and the increasing number, the realities of the economic consequences for ordinary Russians, the realities of the horrific scenes of hospitals and schools being bombed next door in Ukraine, and of civilian casualties there as well.”

The news of the generals’ deaths is trickling out, first from Ukrainians, then confirmed by NATO officials, with one death acknowledged by Mr. Putin in a speech. They have been identified as Maj. Gen. Andrei Kolesnikov, a commander from Russia’s eastern military district; Maj. Gen. Vitaly Gerasimov, first deputy commander of the 41st Combined Arms Army; and Maj. Gen. Andrei Sukhovetsky, deputy commander of the 41st Combined Arms Army.

Western officials say that around 20 Russian generals were in Ukraine as part of the war effort, and that they may have pushed closer to the front to boost morale.

“Three generals already — that’s a shocking number,” Michael McFaul, the former United States ambassador to Russia, said in an interview.

On Wednesday, Ukrainian officials reported that a fourth general, Maj. Gen. Oleg Mityaev, the commander of the 150th motorized rifle division, had been killed in fighting.

Two American military officials said that many Russian generals are talking on unsecured phones and radios. In at least one instance, they said, the Ukrainians intercepted a general’s call, geolocated it, and attacked his location, killing him and his staff.

If Russian military deaths continue to rise, the kinds of civic organizations that called attention to troop deaths and injuries during the Soviet invasion of Afghanistan could once more come to prominence.

But the Russian toll, some military specialists and lawmakers say, is unlikely to change Mr. Putin’s strategy.

“It is stunning, and the Russians haven’t even gotten to the worst of it, when they hit urban combat in the cities,” Representative Jason Crow, Democrat of Colorado and a member of the House Armed Services and Intelligence committees, said in an interview.

“I don’t think it’ll have an impact on Putin’s calculus,” Mr. Crow said. “He is not willing to lose. He’s been backed into a corner and will continue to throw troops at the problem.”

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