Donald Trump made a triumphant return to the White House on Wednesday, where outgoing president Joe Biden offered a show of civility to the bitter rival who denied him the same courtesy four years ago.

Trump's visit came as Republicans were declared the majority party in the House of Representatives to give him complete control of Congress -- and as he announced a string of hardline picks for his top team including firebrand Matt Gaetz as attorney general.

The US president and president-elect shook hands in front of a roaring fire in the Oval Office, with Biden restoring a tradition that Trump broke when he refused to recognize his 2020 defeat by Biden.

"Welcome back," Biden, 81, said as he congratulated the 78-year-old Trump -- the man he has repeatedly branded a danger to democracy -- and pledged a smooth transfer of power.

Biden, who dropped out of the election in July but saw his successor Kamala Harris lose to Trump last week, said he would do "everything we can to make sure you're accommodated."

As the two presidents with a combined age of 159 years shook hands, Biden appeared to look down, while Trump leaned forward and looked him in the eyes.

Trump riled up a mob that attacked the US Capitol in 2021 and ran a brutal and divisive election campaign this year -- but sought to strike a courteous tone on his return visit to the White House.

- 'Politics is tough' -

"Politics is tough, and in many cases it's not a very nice world. It is a nice world today and I appreciate it very much," said Trump, the 45th US president and soon to be the 47th.

Trump added that the transfer of power would be "smooth as you can get."

White House spokeswoman Karine Jean-Pierre later said the talks lasted nearly two hours and were "very cordial, very gracious."

Biden in particular stressed to Trump, who has been skeptical about US support for Ukraine, the need to stand with Kyiv against Russia, National Security Advisor Jake Sullivan said.

Trump will however have almost complete control over the levers of the US government, after the Republicans added to their control of the Senate with a majority in the US House of Representatives.

The billionaire tycoon is now moving fast to appoint a team -- with ultra-loyalists taking key posts.

Hours after the polite show of the Biden meeting, Trump named right-wing Florida lawmaker Gaetz as his top legal official, rewarding the loyalty of a staunch ally who has defended him in his court battles and impeachment fights.

Gaetz resigned from his seat in Congress after Trump's bombshell announcement.

Trump also named former Democratic congresswoman Tulsi Gabbard -- who has opposed US support for Ukraine and met Syria's president Bashar al-Assad -- as his incoming director of national intelligence.

Trump said Gaetz would "end Weaponized Government" in a post widely viewed as an indicator of how strongly the president-elect will seek legal retribution against his opponents.

Gaetz however faces a stormy confirmation process, as he still faces a US congressional ethics panel probe into allegations of sex trafficking and having sex with a minor.

- Third Trump term? -

In a more conventional pick, Trump on Wednesday named Florida senator and China hawk Marco Rubio as his Secretary of State.

But his nomination of Fox News host Pete Hegseth as his defense secretary on Tuesday has also raised eyebrows, given the former veteran's lack of experience in managing anything on the scale of the world's most powerful military.

Trump has meanwhile named the world's richest man and key ally Elon Musk as head of a new group aimed at slashing government spending.

Space X, Tesla and X boss Musk accompanied Trump to Washington on Wednesday from Florida, where the president has spent the week since the election at his Mar-a-Lago resort.

Meeting Republicans at a Washington hotel ahead of the White House meeting, an ebullient Trump suggested that he could even be open to a third term in office -- which would violate the US constitution.

"I suspect I won't be running again unless you say, 'He's good, we got to figure something else,'" he said, drawing some laughter.