Russia's Defense Ministry denied the claim, state-sponsored Sputnik News said.
Lt. Gen. Stephen Townsend, the top US commander in the fight against ISIS in Syria and Iraq, said ISIS fighters had withdrawn from the towns and Syrian-Arab coalition troops had moved in.
US forces serving in an advisory role witnessed the Russian and Syrian airstrikes, Townsend said.
Quick calls to Russian forces through "deconfliction channels" stopped the bombing, he said.
But Moscow's Defense Ministry said neither Russian nor Syrian warplanes struck Manbij or any areas designated by US commanders.
Russia has argued that the United States has not always coordinated its own bombing of targets.