US President-elect Joe Biden's narrow victory in Georgia has been officially certified by Republican Secretary of State Brad Raffensperger.
It comes as legal efforts by Donald Trump's allies to challenge his defeat were dismissed in three other states.
The Democrat beat his Republican rival in Georgia by 12,670 votes, according to the audit required by state law.
Mr Raffensperger on Friday said he was disappointed that his party lost but that "numbers don't lie".
Mr Biden is set to take office in January as the 46th US president.
Mr Biden's victory margin in the public vote overall stands at more than 5.9 million. His victory in the US Electoral College system, which determines who becomes president, is projected to be 306 to 232 - far above the 270 he needs to win.
Mr Trump has so far refused to concede and has made allegations of widespread electoral fraud, without providing any evidence.
The latest defeat comes as he has summoned Michigan state lawmakers to the White House on Friday ahead of that state's deadline to certify election results.
White House spokeswoman Kayleigh McEnany denied that Mr Trump was holding a campaign "advocacy meeting" with the lawmakers, saying it was instead a routine check-in with local officials.
Also on Friday, Mr Trump gave a briefing from the White House on drug pricing, where he again falsely claimed to have won the election. In his first public appearance in a week, he took no questions and seemed to imply he knew another administration would take over soon.
"There will never be anything like this. I just hope they keep it," he said touting new rules aimed as reducing prescription drug costs.
What happened in Georgia?
Mr Raffensperger said on Friday that the result had been certified, posting the result to the secretary of state's website.
On Thursday, Mr Raffensperger - who oversees the election process - said the hand audit of ballots had not altered Mr Biden's victory in the state.
"Georgia's historic first statewide audit reaffirmed that the state's new secure paper ballot voting system accurately counted and reported results," he said in a statement.
On Friday, the self-proclaimed Trump supporter went on to say: "Like other Republicans. I'm disappointed, our candidate didn't win Georgia's electoral votes.
"I live by the motto that numbers don't lie. As secretary of state, I believe that the numbers that we have presented today are correct."
The Democrats' victory is their first in a presidential race in Georgia since Bill Clinton was elected in 1992.
The recount found the error rate was no greater than 0.73% in any county and Mr Biden's margin of victory over Mr Trump remained at under 0.5%. The results will be certified on Friday.
Trump campaign senior legal adviser Jenna Ellis said the audit had gone "exactly as we expected" because, she said without evidence, the state had recounted illegal ballots.
But Gabriel Sterling, a Republican who serves as Georgia's voting system implementation manager, told CNN on Thursday: "One of the big complaints is these machines somehow flipped votes or changed votes or did stuff. They didn't, at least not in Georgia. We proved it."
During the audit this week, nearly 6,000 untallied votes were found - paring back Mr Biden's lead slightly - but they were the result of human error and not fraud, Mr Sterling said.
Officials in Floyd County have fired their election manager over the matter, local media reported on Thursday.
What did Mr Biden say?
He was speaking after a virtual meeting with governors, including Democrats and Republicans, about the coronavirus crisis on Thursday.
Asked about Mr Trump's lack of concession, Mr Biden said the president was sending "incredibly damaging messages... to the rest of the world about how democracy functions" and that he would be remembered "as being one of the most irresponsible presidents in American history".
"It's hard to fathom how this man thinks," he continued, adding: "It's just outrageous what he's doing."
Of the election result, the president-elect - who is due to take office in January - said: "The vast majority of people believe it's legitimate."
Republican Senator Mitt Romney, who lost to Barack Obama in 2012, echoed Mr Biden in a tweet, slamming Mr Trump's "overt pressure on state and local officials to subvert the will of the people and overturn the election".
"It is difficult to imagine a worse, more undemocratic action by a sitting American President," he wrote.
What of the legal challenges?
Republicans lost their final lawsuit in Georgia as a court rejected their effort to block the results' certification, which happened on Friday. The judge who dismissed the case was appointed by Mr Trump last year.
In Arizona, a judge rejected a lawsuit filed last week by the state Republican Party seeking a new audit of ballots in Maricopa County, home to Phoenix - the state capital and largest city.
In Pennsylvania, the Trump campaign lost their bid in state court to throw out more than 2,000 postal ballots.
At a Thursday briefing, Mr Trump's lawyer Rudy Giuliani continued to lay out unsubstantiated conspiracy theories and accusations of electoral fraud.
He railed against the reporting of his team's legal challenges, saying the media had shown an "irrational pathological hatred for the president".
Mr Giuliani also said the campaign was withdrawing its last remaining lawsuit in Michigan. He said it had achieved its aim of stopping the certification of the result in one key county.
However, the vice-chairman of Wayne County's canvassing board said an attempt by its two Republican members to rescind their earlier certification of the result was invalid, and the certification was binding.
One of the Republicans said Mr Trump had called her personally after the vote had been certified "to make sure I was safe".
Mr Biden won the county by a huge margin, according to unofficial results, and prevailed in Michigan by about 146,000 votes.
What could Trump's next move be?
One possibility that US media are speculating on is that he will try to get Republican-friendly state legislatures in key states to override the choice of voters and instead select members of the US Electoral College who would be favourable to the president.
Mr Trump has invited Michigan's Republican lawmakers to the White House on Friday, hinting at a possible change in tactics.
Instead of winning by direct popular vote, a US president must accumulate a majority of "electors" that each state is designated according to its congressional representation.
Most states determine these based on who won the popular vote there.
But federal law says statehouse legislators have the power to pick electors if the state has "failed to make a choice".
This would appear a long shot as no evidence of electoral fraud has been shown and to potentially disenfranchise millions of voters would spark uproar.
Reuters news agency quoted one source familiar with the Trump strategy as saying it was now a "more targeted approach towards getting the legislators engaged".
But one of the Michigan lawmakers going to the White House, Mike Shirkey, said earlier this week that the legislature appointing electors was "not going to happen".