The lawsuit, filed by Trump ally and Congressman Mike Kelly, among others, sought to immediately revoke the already certified results.
“The request for a precautionary measure presented to Judge Alito and referred by him to the Court is denied,” the statement from the Supreme Court read.
There were no dissidents noted, suggesting that the decision not to revoke the results was unanimous.
The Trump campaign has filed and lost more than 50 lawsuits after the election, focused on swing states like Pennsylvania, Georgia, Michigan and Arizona.
But this is the first case of its kind to be appealed to the Supreme Court.
The tweet was published hours before the Supreme Court ruling.
The case was brought despite a flat dismissal it received from an appeals court late last month.
“Free and fair elections are the lifeblood of our democracy,” wrote Judge Stephanos Bibas.
“Voters, not lawyers, choose the president.”
Judge Bibas was appointed by Trump himself.
Meanwhile, Texas Attorney General Ken Paxton filed a lawsuit in Supreme Court against the states of Georgia, Michigan, Pennsylvania and Wisconsin.
Paxton has accused the states of participating in electoral irregularities and has tried to put the election results in the hands of the legislatures of those states.
He accused the four states of “exploiting the COVID-19 pandemic” to justify changes to electoral procedures in an effort to skew the outcome.
“The states violated the statutes promulgated by their duly elected legislatures, thereby violating the Constitution.”
His Michigan counterpart, Attorney General Dana Nessel, described his lawsuit as a “publicity stunt.”
“The Michigan issues raised in this lawsuit have already been thoroughly litigated and rejected outright in state and federal courts, by appointed judges from both political parties,” he said.
“Mr. Paxton’s actions are beneath the dignity of the attorney general’s office and the people of the great state of Texas.”
Wisconsin Attorney General Josh Kaul described Paxton’s lawsuit as “really embarrassing.”
Paxton is currently under investigation by the FBI on allegations of bribery and abuse of power by eight former aides.
He was elected as the top law enforcement officer in Texas in 2016 despite the fact that he has been charged with securities fraud. He has yet to be tried five years after being charged.
Joe Biden will be formally named president-elect when the electoral college meets next week.
He will be sworn in as president on January 20. Trump has declined to say whether he will attend the inauguration.