"The application for stay presented to the Chief Justice and by him referred to the Court is denied," the court filing said on Thursday.
The Republican Party in Pennsylvania previously made two attempts to have the US Supreme Court block a deadline extension for mail-in ballots.
Early voting for the US presidential election ends this week as Election Day approaches on Tuesday.
Earlier, the Pennsylvania Republican Party attempted to challenge a decision by the Pennsylvania Supreme court to extend the deadline for mail-in ballots in the state to November 6-three days after Election Day. The decision came after the Republican Party and President Donald Trump's statement that the practice of sending out ballots and extending deadlines can potentially lead to vote harvesting as well as the falsification of election results.