In a televised appearance just before 11 p.m. Friday in Wilmington, Del., Biden said, "We're going to win this race."
Standing alongside his running mate, California Sen. Kamala Harris, Biden said he is on track to win over 300 electoral votes and urged patience while the final ballots are counted.
"We have to remain calm, patient, let the process work out as we count all the votes."
Biden said he would not wait to get to work on the nation's problems, most urgently an economic crisis and the COVID-19 pandemic. He and Harris have begun meeting with health and economic experts.
"On day one, we're going to put our plan to control this virus into action," he said.
In Pennsylvania, Biden grew his lead to about 28,000 votes, according to state figures late Friday.
About 21,000 mail ballots remained to be tabulated in Philadelphia County, according to Pennsylvania's Department of State, with a small number of precincts yet to report final numbers in in-person voting. City Commission Chairwoman Lisa Deeley said in a noontime news conference, cautioning it may take "several days" to complete the count.
Statewide, some 89,000 mail ballots cast have yet to be counted, just over 3% of the mail-in ballot total.
The largest chunk of outstanding mail-in ballots were in Allegheny County. About 29,000 of them are had a printing error, and in some cases, voters either submitted a new, corrected mail ballot or received a provisional ballot during in-person voting.
As elections officials closed in on finishing the mail ballot counting, their attention with then turn toward provisional ballots. These ballots likely will take time to evaluate, verify and count.
Meanwhile, the U.S. Supreme Court on Friday ordered that all mail ballots that arrived after Election Day be segregated and counted. The totals from those ballots must be kept separate, though.
Pennsylvania Republicans had asked the U.S. Supreme Court for the order earlier in the day. Pennsylvania Secretary of State Kathy Boockvar said the late-arriving ballots were already being separated and had not yet been counted.
The state Supreme Court ruled in September that all mail-in ballots postmarked by Nov. 3 would be accepted and counted up to three days after Election Day.
A total of 71 electoral votes were still up for grabs in six states -- Pennsylvania (20), Georgia (16), Arizona (11), North Carolina (15), Nevada (6) and Alaska (3). There is also one electoral vote in a Maine district that has not been projected.
In Georgia, Biden's lead grew by more than 4,000 votes after officials updated their count Friday evening.
Trump, who has made accusations of voter fraud without any supporting evidence, would need to secure both Georgia and Pennsylvania to win re-election.
"We're not seeing any widespread irregularities," voting system implementation manager Gabriel Sterling said. "We're investigating any credible accusation with any real evidence behind it."
Georgia Secretary of State Brad Raffensperger said Friday afternoon that a recount is all but certain.
"The final tally in Georgia at this point has huge implications for the entire country," he said. "The stakes are high and emotions are high on all sides. We will not let those debates distract us from our work. We will get it right, and we will defend the integrity of our elections."
In Georgia, a recount is mandatory if the difference between the candidates is 0.5% or smaller. Biden presently has a lead of less than 0.1%, with a few thousands ballots left to count.
Only about 4,000 votes remain to be counted statewide, Sterling told reporters. About 3,500 of those votes were in Democratic-leaning Gwinnett County in suburban Atlanta, he said.
In Nevada, Biden grew his lead over Trump in new votes tabulated Friday.
Biden, who began Friday with a lead of about 11,000 votes, increased the margin to more than 22,600, according to the updated official numbers.
Nevada began Friday with more than 190,000 ballots remaining to be counted -- 90% of which were in Clark County, which contains Las Vegas and is heavily Democratic.
In Arizona, Secretary of State Katie Hobbs said counting will extend to the weekend with 250,000 to 270,000 ballots remaining. About half of those are in Maricopa County.
Biden leads with 1,604,000 votes to Trump's 1,537,000, a 1% or nearly 30,000-vote margin.
In North Carolina, Trump holds a lead of about 80,000 votes, according to official state data.