Michigan certified its election results. President-elect Joe Biden is expected to announce his picks for key roles in his cabinet and administration, some of whom would make history. Senator Dianne Feinstein said she would relinquish the top Democratic spot on the Judiciary Committee next year.

Emily Murphy, the administrator of the General Services Administration, on Monday formally designated President-elect Joseph R. Biden Jr. as the apparent winner of the presidential election, providing federal funds and resources to begin a transition and authorizing his advisers to begin coordinating with Trump administration officials.

President Trump said on Twitter Monday night that he was authorizing his staff to begin “initial protocols” for the transition process. He did not concede the election, and vowed to persist with efforts to undermine the vote that have so far proved fruitless. But he acknowledged in his most explicit terms yet that his time in the White House was coming to an end.

Ms. Murphy’s decision came after several more senior Republican lawmakers denounced her delay in allowing the peaceful transfer of power to begin, a delay that Mr. Biden and his top aides said was threatening national security and the ability of the incoming administration to effectively plan for combating the ongoing pandemic.

In her letter, Ms. Murphy said she was “never directly or indirectly pressured by any executive branch official — including those who work at the White House or the G.S.A.” She defended her delay by saying that she did not want to get ahead of the constitutional process of counting votes and picking a president.

“I do not think that an agency charged with improving federal procurement and property management should place itself above the constitutionally-based election process,” she wrote in a letter to Mr. Biden’s transition.

Mr. Trump, in a tweet shortly after Ms. Murphy’s announcement, made clear that he accepted it.

“Our case STRONGLY continues, we will keep up the good fight, and I believe we will prevail!” Mr. Trump wrote. “Nevertheless, in the best interest of our Country, I am recommending that Emily and her team do what needs to be done with regard to initial protocols, and have told my team to do the same.”

Ms. Murphy refuted Mr. Trump’s assertion that he directed her to make the decision, saying in her letter that “I came to my decision independently, based on the law and available facts.”

In her letter, Ms. Murphy said she made her decision on Monday because of “recent developments involving legal challenges and certifications of election results,” likely referring to the certification of votes by election officials in several states and a string of court decisions that have rejected Mr. Trump’s challenges.

Ms. Murphy’s decision was first reported on CNN Monday afternoon, as reported by The New York Times.