The 11 senators and senators-elect, led by Ted Cruz, want a 10-day delay to audit the unsubstantiated allegations.
The move is not expected to succeed as most senators are expected to endorse Mr Biden in the 6 January vote.
President Donald Trump has refused to concede, repeatedly alleging fraud without providing any evidence.
His legal efforts to overturn results have been overwhelmingly rejected by the courts. He has only one minor win, concerning a small number of postal ballots in Pennsylvania, one of the states Mr Biden won in last year's race.