WASHINGTON — The federal government recognized President-elect Joe Biden as the “apparent winner” of the Nov. 3 election, formally starting the transition of power after President Donald Trump spent weeks testing the boundaries of American democracy. Trump relented after suffering yet more legal and procedural defeats in his seemingly futile effort to overturn the election with unsubstantiated claims of fraud.

Trump still refused to concede and vowed to continue to fight in court after General Services Administrator Emily Murphy gave the green light Monday night for Biden to coordinate with federal agencies ahead of his Jan. 20 inauguration. Trump tweeted that he was directing his team to cooperate on the transition.

The fast-moving series of events seemed to let much of the air out of Trump’s frantic efforts to undermine the will of the people in what has amounted to a weekslong stress test for the nation’s confidence in the political system and the fairness of U.S. elections. Those efforts haven’t ended and are likely to persist well beyond his lame duck presidency.

Murphy, explaining her decision, cited “recent developments involving legal challenges and certifications of election results.”

She acted after Michigan on Monday certified Biden’s victory in the battleground state and a federal judge in Pennsylvania tossed a Trump campaign lawsuit on Saturday seeking to prevent certification in that state.

It also came as an increasing number of Republicans were publicly acknowledging Biden’s victory, after weeks of tolerating Trump’s unsubstantiated claims of fraud. The Republican president had grown increasingly frustrated with the flailing tactics of his legal team.

Joe Biden defeated Trump and was declared the 46th President of the United States on Saturday morning.

In recent days, senior Trump aides including chief of staff Mark Meadows and White House counsel Pat Cipollone had also encouraged him to allow the transition to begin, telling the president he didn’t need to concede but could no longer justify withholding support to the Biden transition.

Meadows sent a memo late Monday to White House staffers saying their work was not yet finished and that the administration would “comply with all actions needed to ensure the smooth transfer of power,” according to a person who received it.

Yohannes Abraham, executive director of the Biden transition, said the decision “is a needed step to begin tackling the challenges facing our nation, including getting the pandemic under control and our economy back on track.”

Murphy, a Trump appointee, had faced bipartisan criticism for failing to begin the transition process sooner, preventing Biden’s team from working with career agency officials on plans for his administration. The delay denied the Democratic president-elect access to highly classified national security briefings and hindered his team’s ability to begin drawing up its own plans to respond to the raging coronavirus pandemic.

Murphy insisted she acted on her own.

“Please know that I came to my decision independently, based on the law and available facts. I was never directly or indirectly pressured by any Executive Branch official — including those who work at the White House or GSA — with regard to the substance or timing of my decision,” she wrote in a letter to Biden.

Max Stier, president and CEO of the nonpartisan Partnership for Public Service, criticized the delay but said Biden’s team would be able to overcome it.

“Unfortunately, every day lost to the delayed ascertainment was a missed opportunity for the outgoing administration to help President-elect Joe Biden prepare to meet our country’s greatest challenges,” he said. “The good news is that the president-elect and his team are the most prepared and best equipped of any incoming administration in recent memory.”

Senate Democratic leader Chuck Schumer said the GSA action “is probably the closest thing to a concession that President Trump could issue.″ Noting that the nation “faces multiple crises that demand an orderly transition,″ Schumer urged Democrats and Republicans to “unite together for a smooth and peaceful transition that will benefit America.″

Murphy’s action came 90 minutes after Michigan election officials certified Biden’s 154,000-vote victory in the state. The Board of State Canvassers, which has two Republicans and two Democrats, confirmed the results on a 3-0 vote with one GOP abstention. Trump and his allies had hoped to block the vote to allow time for an audit of ballots in Wayne County, where Trump has claimed without evidence that he was the victim of fraud. Biden crushed the president by more than 330,000 votes there.