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.
