The latest in a series of attempts by allies of President Donald Trump to overturn the November US election result has failed.
A Texas judge rejected the case, brought by Republican Louie Gohmert, seeking to stop Vice-President Mike Pence from certifying the final result.
Lawyers for Mr Pence had asked for the case to be thrown out on Thursday.
President-elect Joe Biden is due to take office on 20 January. Mr Trump is yet to concede.
Mr Gohmert, a Republican congressman, told Newsmax TV that he planned to appeal against the verdict.
Mr Trump's friends and colleagues in the Republican party have presented dozens of legal challenges to the November outcome which delivered a decisive win to Mr Biden.
His victory was announced after days of vote-counting that took longer than in recent years because of the huge number of postal ballots cast due to the coronavirus pandemic.
Mr Trump has made numerous unsubstantiated claims that Mr Biden's win, which saw the president-elect gain 306 electoral college votes to his rival's 232, was fraudulent.
The electoral college is a system whereby each US state has an allocated number of points that is granted to the overall winner in each state. The candidate who gains the majority wins the presidency.
Congressman Gohmert's case sought to allow Vice-President Mike Pence to reject some electoral college votes when they are ratified by Congress on 6 January.
The vice-president presides over the vote certification in Congress in a ceremonial role that involves opening and tallying the envelopes containing electoral college votes before announcing the result.
Mr Gohmert's case aimed to expand that role to allow Mr Pence to cast judgement on the validity of the votes and potentially replace votes for Mr Biden with ones for Mr Trump.
But Judge Jeremy Kernodle, who was appointed to the Texas court in 2018 by Mr Trump, rejected the case, saying it was based on speculative events.
On Thursday a lawyer from the US Justice Department representing Mr Pence urged Mr Gohmert to drop the case, suggesting that it was not the vice-president's office that should be scrutinising the outcome.
Although most Republicans in Congress are expected to vote in favour of certifying the results, a small number including Senator Josh Hawley, say they plan to object. But their vote is not expected to change the outcome.
Mr Biden is due to be sworn in as president on 20 January at a scaled-back ceremony with just 1,000 tickets available due to Covid-19 precautions.