Donald Trump made a triumphant entrance to cap the first day of the Republican National Convention, receiving a raucous ovation from the party faithful days after surviving an assassination attempt that has reshaped the US presidential contest.

The former president walked into the Fiserv Forum in downtown Milwaukee to an uproarious response, his ear heavily bandaged from having been grazed by a bullet, hours after he was officially nominated to be the party’s 2024 standard-bearer.

“Fight! Fight! Fight!” the crowd chanted while pumping their fists, a reference to Trump’s response in the moments after he was shot.

Uncharacteristically subdued, Trump waved from a box where he sat alongside his newly anointed running mate, US Senator JD Vance.

The attack at a Trump rally in Pennsylvania on Saturday, which killed a supporter, underscored the nation’s deeply fractured political landscape ahead of the November 5 election between Trump and Democratic President Joe Biden.

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Biden, who has portrayed Trump as a threat to US democracy, condemned the shooting and urged Americans to rely on the ballot box, not violence, to resolve their differences.

Authorities were still trying to identify a motive for the shooting after the gunman was killed by the US Secret Service.

In an NBC interview broadcast opposite the convention on Monday evening, Biden said he made a mistake by saying Trump should be put in the “bullseye” last week but added that Trump has frequently employed violent rhetoric on the campaign trail.

Biden has ordered an independent review to determine how the gunman could have come so close to killing Trump despite the Secret Service’s heavy security presence.

The four-day convention will culminate with Trump’s prime-time address on Thursday when he formally accepts the party’s nomination to face Biden in a rematch of their 2020 race.

The assassination attempt, followed by the convention, has pushed Biden to the background after weeks of speculation about whether he might drop out of the race following a disastrous debate performance last month.

Biden again rejected the notion on Monday when pressed by NBC’s Lester Holt, focusing instead on the myriad falsehoods Trump unleashed during the debate.

The president has stepped up his unscripted appearances to try to demonstrate his capability but has yet to assuage some Democrats’ fears about his reelection chances.

Trump’s selection of Vance, the 39-year-old author of the best-selling “Hillbilly Elegy”, completed the Ohio senator’s transformation from an outspoken Trump critic to one of his most loyal supporters.

Vance, who shares Trump’s affinity for political brawling, is likely to energise core Republicans, but it is less clear whether he can broaden the ticket’s appeal to moderate and independent voters wary of another Trump term.

Biden called Vance a Trump “clone” on Monday, and Democrats pounced on Vance’s opposition to abortion rights, an issue that has proven damaging to Republicans.

In a Fox News appearance on Monday night, Vance said he backed Trump’s position that each state should decide for itself whether to permit abortion.

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The race between Trump and Biden remains close, according to public opinion polls, though Trump leads in several swing states likely to decide the election.

Monday began with the latest in a string of recent legal victories for Trump when US District Judge Aileen Cannon threw out federal charges in Florida accusing him of illegally retaining classified documents.

Trump is due to be sentenced in New York in September for trying to cover up a hush money payment to porn star Stormy Daniels in the weeks before his 2016 election victory.

But his other two indictments on federal charges in Washington and state charges in Georgia — both related to his efforts to overturn his 2020 election defeat — are mired in delays and could be imperilled after the US Supreme Court ruled in July that he had immunity for many of his official acts as president.