Donald Trump met with Joe Biden on Wednesday and promised a transfer of power that is “as smooth as it can get”, as the outgoing US president pledged his administration’s every possible resource to pave the way for his successor.

The two men, longtime political rivals who must now work together again to pass the reins of power, shook hands as they met in the Oval Office. Introducing Trump as both a former president and now president-elect, Biden congratulated him on his victory.

“We’re looking forward to having, like we said, a smooth transition. We’ll do everything we can to make sure you’re accommodated, what you need and we’re going to get a chance to talk about some of that today,” Biden said. “Welcome back.”

Despite Trump’s many excoriating comments toward Biden over the years, he thanked the president for the warm reception he received at the White House.

“Politics is tough, and it’s, in many cases, not a very nice world, but it is a nice world today, and I appreciate very much a transition that’s so smooth. It’ll be as smooth as it can get. And I very much appreciate that, Joe,” Trump said.

Reporters attempted to shout questions at Biden and Trump, but both men ignored the queries. The meeting continued for roughly two hours after journalists were escorted out of the Oval Office.

The White House press secretary, Karine Jean-Pierre, offered few specifics about the meeting, but she noted that Biden described Trump as “gracious” and prepared with “a detailed set of questions”.

“It was indeed very cordial, very gracious and substantive,” Jean-Pierre said. “National security was discussed. Domestic policy issues were discussed.”

Before meeting with Biden, Trump addressed House Republicans on Capitol Hill, celebrating his party’s victories up and down the ballot last week while suggesting he might seek a third term as president.

“I suspect I won’t be running again, unless you say, ‘He’s good, we got to figure something else,’” Trump said, sparking laughter from fellow Republicans in the room.

Trump has repeatedly floated the idea of extending his tenure, even though the US constitution bars presidents from serving a third term.

Introducing Trump on Wednesday, the Republican speaker of the House, Mike Johnson, praised the president-elect as a “singular figure in American history”.

“They used to call Bill Clinton the comeback kid. [Trump] is the comeback king,” Johnson said.

Elon Musk joined Trump at the meeting with House Republicans, sitting in the first row, according to attenders. On Tuesday, Trump named Musk and the former presidential candidate Vivek Ramaswamy as co-leaders of a new Department of Government Efficiency. The announcement intensified concerns over how Trump and Musk, known for his slash-and-burn approach to cutting company expenses, might overhaul the federal workforce. Also on Tuesday, Trump named Pete Hegseth, a veteran and Fox News host with no political experience, to lead the Department of Defense.

Trump continued his series of cabinet announcements on Wednesday with the news that Marco Rubio, a Republican senator of Florida, would be nominated as secretary of state. He also named Tulsi Gabbard, a former Democratic congresswoman, as director of national intelligence and Matt Gaetz, a Republican congressman of Florida, as attorney general. All three nominations are subject to Senate approval, and Gabbard and Gaetz specifically may face numerous hurdles to confirmation.

As of Wednesday, Republicans had already won a majority in the Senate, but the House remained up for grabs as ballot-counting continued in 12 uncalled races. However, House Republicans appear poised to capture a narrow majority.

Trump has already tapped at least three House Republicans for senior roles in his administration. In addition to Gaetz, Elise Stefanik will be nominated as ambassador to the United Nations and Mike Waltz, a Florida representative, will serve as his national security adviser. Republicans currently hold a razor-thin four-seat majority in the House, and if the outcome of vote counts remains as it stands today, a Republican speaker in 2025 would also have a four-seat majority.

Johnson has said he expects Republicans to end up with a larger majority. But each Republican appointment or resignation from the House – as Governor-elect Kelly Armstrong of North Dakota must do – diminishes that majority.

“We have an embarrassment of riches,” Johnson said on Tuesday. “We have a really talented Republican conference. We’ve got really competent, capable people here. Many of them could serve in really important positions in the new administration, but President Trump fully understands and appreciates the math here, and it’s just a numbers game.”

The meeting between Biden and Trump on Wednesday reflected a return to a traditional transfer of power, after the custom was somewhat abandoned in 2020. Underscoring the acrimony of the 2020 election, Trump eschewed the meeting after being defeated by Biden.

Melania Trump was also invited to meet with the first lady, Jill Biden, but she declined the invitation. According to the White House, the first lady offered Trump’s team “a handwritten letter of congratulations for Mrs Trump, which also expressed her team’s readiness to assist with the transition”.