President Joe Biden and Donald Trump both advocated for a "smooth" transfer of power during their first meeting since Trump won the presidential election last week.

Conversing in the White House's Oval Office, Biden said he was "looking forward to having... a smooth transition" and told the president-elect his team would "do everything we can to make sure you're accommodated".

Trump responded by thanking Biden and saying: "I appreciate very much a transition that's so smooth it'll be as smooth as it can get".

The cordial exchange marked a contrast from the last presidential election, when Trump failed to invite Biden to the White House after Biden's victory in 2020, bucking tradition.

Trump falsely claimed that the election was rigged, a claim he repeated often during this most recent election campaign.

The meeting on Wednesday marked the first time Trump had set foot in the White House in four years.

The two leaders took part in a quick photo-op, before sitting down in front of a burning fireplace, where they exchanged pleasantries in front of the cameras.

"Welcome, welcome back," Biden told Trump.

"Politics is tough, and it's 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 responded.

While tradition prevailed with Biden and Trump's meeting, the same was not true for First Lady Jill Biden and Trump's wife, Melania.

Mrs Trump did not accompany her husband to the White House. The wife of the president-elect and the current first lady usually have tea while their husbands meet.

Mrs Biden instead stood alongside the president as he welcomed Trump, and handed him a hand-written letter addressed to Mrs Trump.

In the letter, she expressed "her team's readiness to assist with the transition", according to the White House.

Following the meeting in front of the cameras, Trump and Biden retired to a more private setting where they spoke for nearly two hours.

They are expected to have discussed a number of issues, ranging from US foreign policy to the logistics of handing over power.

According to the White House, Trump's incoming chief of staff Susie Wiles and Biden's chief of staff Jeff Zients joined the two for part of the meeting, CBS News, the BBC's US media partner, reports.

As Trump and Biden met, Senate Republicans convened to elect their new majority leader, picking South Dakota Senator John Thune after two rounds of voting.

Also on Wednesday afternoon, CBS projected Republicans had won control of the House of Representatives, granting Trump support in both the House and the Senate.

The president-elect is still working on selecting new members of his administration ahead of his 20 January inauguration.

His latest appointments include Fox News host Pete Hegseth as defence secretary, and billionaire supporter Elon Musk in a new cost-cutting role.

About 4,000 political appointments are expected to be made ahead of Trump's inauguration in late January. The process can take months.