A joint session of the Senate and House of Representatives met on Thursday to hear the results of the Electoral College that officially chooses the president.
But about 20 Democrats from the House joined Senator Barbara Boxer to contest the result in Ohio.
Boxer demanded a debate on irregularities in Ohio, including long lines of people who could not cast votes on 2 November and a reported lack of voting machines in heavily-Democratic districts.
"I hated inconveniencing my friends, but I think it is worth a couple of hours to shine some light on the issues," she said.
The protests temporarily halted the tallying of the electoral college votes. The Senate rejected the challenge by a vote of 1-74 and the House by 31-267.
Both chambers are controlled by Bush's Republican party.
Senator Ted Kennedy said Democrats were not seeking to overturn Bush's victory, but to call attention to an injustice.
"As in 2000, the votes of many who wanted to vote were not, in fact, counted," the Democratic lawmaker said.
Kerry is seeking electoral reforms,
not to contest the result
Neither Democratic presidential candidate John Kerry nor the party leadership has contested the election result, but there have been widespread calls for electoral reform to make voting procedures more uniform across the US and ensure that every vote gets counted.
"No American citizen should wake up the morning after the election and worry their vote wasn't counted," Kerry wrote in a letter released on Wednesday.
"Despite widespread reports of irregularities, questionable practices by some election officials and instances of lawful voters being denied the right to vote, our legal teams on the ground have found no evidence that would change the outcome of the election," Kerry's statement added.