In a one-sentence denial on Tuesday, the justices left intact a ruling by the Pennsylvania Supreme Court, Xinhua news agency reported.
The petition was led by US Congressman Mike Kelly, a Republican and ally of President Donald Trump, who argued that virtually all of the state’s mail-in ballots were unlawful.
The Pennsylvania Supreme Court tossed the case last month, citing the litigants’ undue delay in bringing the challenge.
The action by the country’s highest court came as states are locking in the results that will lead to next week’s Electoral College vote.
Trump still refuses to concede in the White House race with Biden, a Democrat and former US vice president.
In Pennsylvania, a battleground state which Trump carried four years ago, the certification of election results this year showed Biden won by a margin of 80,555 votes.