Donald Trump has launched a third bid for the White House, firing the starting gun on the 2024 presidential election cycle just one week after midterm elections in which many of the Republicans he endorsed underperformed expectations in races up and down the ballot.

“In order to make America great and glorious again I am tonight announcing my candidacy for president of the United States,” Trump told supporters Tuesday night at Mar-a-Lago, his resort in Palm Beach, Florida.

Standing in the resort’s gilded ballroom in front of more than a dozen American flags and flanked by signs with his slogan “Make America Great Again”, Trump said: “America’s comeback starts right now.”

Minutes before his speech, Trump filed paperwork establishing his candidacy with the Federal Election Commission. He is the first Republican to announce he will run for president in 2024. He is also the first US president to lose his re-election bid, only to try again, in more than a century.

While in office, Trump was impeached twice by the House of Representatives, although he was not convicted in the Senate either time. He is currently embroiled in several legal matters, as well as a congressional probe into his role in the January 6 2021 attack on the US Capitol and efforts to overturn the results of the 2020 presidential election.

Trump’s entrance into the race comes despite several of his handpicked candidates losing in the midterms and a growing chorus of voices from within the Republican party urging him to step aside.

For more than a year, Trump made no secret of his desire to run again in 2024, repeating his baseless claims that the 2020 election was “rigged” and “stolen” from him. But Trump held off on formally launching a campaign until Tuesday, in part at the urging of advisers and Republicans who did not want him to overshadow the midterms.

Following the midterms, Trump faced fresh calls to delay his announcement after many of his blockbuster endorsements — including Pennsylvania Senate candidate Mehmet Oz and Arizona governor hopeful Kari Lake — fell short in their races.

Others made private and public appeals for Trump to step off the political stage and allow a new generation of Republicans to seek the party’s nomination — notably Ron DeSantis, Florida’s governor, who won re-election last week by a landslide 19 points.

A YouGov poll, conducted after last week’s elections and published on Sunday, showed that 42 per cent of Americans who identified as Republicans or leaned towards the Republican party said they would prefer to see DeSantis as their party’s nominee in 2024, compared with 35 per cent who said they preferred Trump.

The Club for Growth, the conservative, low-tax group that once backed Trump but has broken with him of late, released a memo on Monday citing polling of likely Republican voters in Iowa and New Hampshire, showing DeSantis leading the field in both early states that are crucial to winning the party’s nomination.

Among Iowa voters, DeSantis led Trump 48 per cent to 37 per cent, according to the memo, while in New Hampshire, the Florida governor led the former president 52 per cent to 37 per cent.

DeSantis has not yet said whether he will seek the presidency, but broke into a smile when the crowd at his victory party last week appeared to encourage him to run, shouting: “Two more years!”

In public statements and posts on his social media platform Truth Social, Trump has shown little sign of backing down, tearing into DeSantis, Senate minority leader Mitch McConnell and Rupert Murdoch, whose newspapers, notably the New York Post, have thrown their weight behind a possible DeSantis candidacy.

Asked about Trump’s attacks on Tuesday, DeSantis did not mention the former president by name, but said people should “check out the scoreboard from last Tuesday night”.

“One of the things I’ve learned in this job: When you’re leading and getting things done, you take incoming fire. That’s just the nature of it.”

It remains unclear how many Republicans would challenge Trump for his party’s nomination for president. In addition to DeSantis, Mike Pence, his vice-president, has hinted at a run, as has Larry Hogan, the centrist outgoing governor of Maryland. Glenn Youngkin, the former Carlyle executive who was elected governor of Virginia last year, is also reportedly weighing up a bid.

On the other side of the aisle, Joe Biden has not yet formally said that he will run for re-election in 2024. But after Democrats’ better than expected results in the midterms, he sent the strongest signal yet that he will seek a second term, saying: “Our intention is to run again.”

At the same time Trump announced his candidacy in Mar-a-Lago on Tuesday night, Biden was in Bali, Indonesia, convening world leaders for a crisis meeting on the sidelines of the G20 in response to the death of two Poles who were killed by what Warsaw said was a “Russian-made missile”.

The White House later posted a video on Biden’s Twitter page with the caption: “Donald Trump failed America.”

On Monday, the US Supreme Court cleared the way for the January 6 committee to obtain phone records of Kelli Ward, who chairs the Republican party in Arizona, one of several states where Trump sought to have the election results thrown out.

Additional reporting by Caitlin Gilbert in New York