Donald Trump made a triumphant entrance during the first night of the Republican National Convention on Monday (Jul 15), receiving a raucous ovation from the party faithful two days after a would-be assassin's bullet grazed his right ear.

Trump walked into the Fiserv Forum in downtown Milwaukee with a thick bandage over the ear as the crowd chanted "Fight! Fight! Fight" and pumped their fists, a reference to his reaction in the moments after he was wounded.

The former president appeared moved by the response as he stood in a box alongside members of his family and Senator JD Vance, Trump's choice for running mate announced earlier in the day.

The four-day convention opened hours after Trump secured a major legal victory when a federal judge dismissed one of his criminal prosecutions.

Trump is due to formally accept the party's nomination in a prime-time speech on Thursday and will face Democratic President Joe Biden in the Nov 5 election.

During the evening session, one speaker after another blamed Biden's economic policies for inflation that has kept prices higher, even as it has eased sharply since peaking in June 2022 in the wake of the COVID-19 pandemic.

Senator Tim Scott, who briefly ran against Trump for the nomination, said divine intervention spared Trump's life.

"Our God still saves," Scott said. "He still delivers and he still sets free. Because on Saturday the devil came to Pennsylvania holding a rifle, but an American lion got back up on his feet and he roared!"

Vance, 39, was a fierce Trump critic in 2016 but has since become one of the former president's staunchest defenders, embracing his false claims that the 2020 election was marred by widespread fraud.

Vance is deeply popular with Trump's core supporters, but it remains to be seen whether he can broaden the ticket's appeal. He shares Trump's aggressive approach to politics, and his conservative statements on issues such as abortion could turn off moderate voters.

Soon after Trump's afternoon announcement, Vance emerged on the convention floor with his wife Usha, shaking hands with and hugging delegates who swarmed the couple. He is scheduled to address the convention on Wednesday.

Biden told reporters at Joint Base Andrews in Maryland that Vance is "a clone of Trump on the issues", while Democrats assailed Vance's record on reproductive rights.

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

Opinion polls show a close race between Trump, 78, and Biden, 81, though Trump leads in several swing states that are likely to decide the election. Trump has not committed to accepting the results of the election if he loses.

The head of the main fundraising super political action committee (PAC) supporting Trump's campaign, Taylor Budowich, said on X that MAGA Inc had raised more than US$50 million on Monday.

Billionaire Elon Musk is planning to donate around US$45 million a month to a new pro-Trump super PAC, the Wall Street Journal reported, citing people familiar with his intentions. Musk endorsed Trump after the assassination attempt on Saturday.

After the assassination attempt, Trump said he was revising his acceptance speech to emphasise national unity, rather than highlight his differences with Biden.

"The speech will be a lot different, a lot different than it would've been two days ago," Trump told the Washington Examiner.

US District Judge Aileen Cannon's decision on Monday to throw out federal charges against Trump for retaining classified documents after leaving the White House was the latest in a string of legal wins for the former president, who 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.

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 significantly limited after the US Supreme Court ruled in July that he had immunity for many of his official acts as president.

"This dismissal of the Lawless Indictment in Florida should be just the first step, followed quickly by the dismissal of ALL the Witch Hunts," Trump said on Truth Social on Monday, also referencing the prosecutions of hundreds of his supporters who stormed the US Capitol on Jan 6, 2021.