The lawsuit, filed on Nov. 9, alleged inconsistent treatment by county election officials of mail-in ballots.
Some counties have informed voters that they can correct minor flaws such as missing “secret envelopes”, while others have not.
The trial also initially alleged that Republican observers were denied access to the ballot count by mail, a claim by election officials. The November 15 campaign dropped allegations of those allegations, but then asked to add them.
Judge Brann had expressed his skepticism about the trial during a hearing on Tuesday.
Pennsylvania officials can certify election results which currently show Mr. Biden winning the state by more than 80,000 votes, the federal judge ruled on Saturday.
“In the United States of America, that cannot justify the denial of the right to vote of just one voter, let alone all voters in its sixth most populous state,” the judge said. “Our people, our laws and our institutions demand more.”
Mr Trump’s team had argued that the US Constitution’s guarantee of equal protection under the law was violated when counties in Pennsylvania took different approaches to inform voters ahead of the election of related technical issues. to their postal ballots.