A further 80,000 have been wounded, National Security Council spokesman John Kirby said, citing newly declassified intelligence.
Half of the dead are from the Wagner mercenary group, the US says.
If accurate, the number of Russian casualties outweighs the city's pre-war population of 70,000.
Moscow has been trying to take Bakhmut since last year in a grinding war of attrition.
The battle for the small city - where only a few thousand civilians remain - has taken on huge symbolic importance for both sides.
Ukrainian officials have also said they are using the battle to kill as many Russian troops as possible and wear down its reserves. However, Ukraine only now controls a small portion of the city.
"Russia's attempt at an offensive in the Donbas largely through Bakhmut has failed," Mr Kirby told reporters. "Russia has been unable to seize any real strategic and significant territory."
"We estimate that Russia has suffered more than 100,000 casualties, including over 20,000 killed in action," he added.
The toll in Bakhmut accounts for losses since the start of December, according to the US figures.
"The bottom line is that Russia's attempted offensive has backfired after months of fighting and extraordinary losses," Mr Kirby said.
He added he was not giving estimates of Ukrainian casualties because "they are the victims here. Russia is the aggressor".
The BBC is unable to independently verify the figures given and Moscow has not commented.