The candidates had been locked in a virtual dead heat for much of Thursday, with each controlling about 49.4 percent of the vote, but with Mr. Trump maintaining a slight lead.
Flipping Georgia, a state last won by a Democrat in 1992, and where Trump won by more than 200,000 votes four years ago, would represent a significant political shift.
The latest batch of mail-in ballots from Philadelphia pulled Biden ahead by more than 5,000 votes in Pennsylvania, putting him in a strong position to win a state that would lift him above the 270 Electoral College votes needed to win the presidency.
Across the state, tens of thousands of ballots are still to be counted, mostly from predominantly Democratic areas.
Trump’s chances have continued to shrink as he continues to claim fraud in the counting of ballots.