Pentagon chief Chuck Hagel, however, warned against resorting to "body counts" to measure progress in the war.
The estimate of how many IS fighters had been taken out by US-led air raids was first cited by Washington's ambassador to Iraq, Stuart Jones, in an interview aired yesterday by Al-Arabia television.
US defense officials reluctantly confirmed the figure but insisted the military was not placing a priority on the measurement, which carried uncomfortable echoes from the Vietnam conflict -- when American commanders cited daily "body counts" to convey progress in the war.
But if accurate, it would suggest the coalition has inflicted astounding damage on the IS group since the air strikes began in Iraq on August 8 and in Syria on September 23.
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The casualty toll would mean bombing raids wiped out roughly 20-30 percent of the IS group's fighting force, which is estimated at between 20,000 to 31,500 fighters, according to the Central Intelligence Agency's estimates released last year.
Hagel told a news conference he could not confirm the 6,000 death toll but said "thousands" of IS fighters had been killed in US-led bombing raids.
However, Hagel, a Vietnam veteran who still carries shrapnel fragments in his chest from his war wounds, said the number of IS militants killed was not a useful gauge for assessing the effect of the air campaign.
"I was in a war where there was a lot of body counts every day. And we lost that war," he said.
Other indicators showed that the IS was on the defensive and under pressure, Hagel said, including signs the jihadists were having trouble recruiting, keeping supply routes open and maintaining communications on the battlefield.