Donald Trump won the formal nomination Monday as the Republican presidential candidate and picked a right-wing loyalist for his running mate, kicking off a triumphalist party convention in the wake of the weekend's failed assassination attempt.

The Milwaukee gathering erupted into cheers as Trump announced 39-year-old Ohio Senator J.D. Vance as his vice presidential pick, rewarding a one-time harsh critic who has become one of his most uncompromising supporters.

"As Vice President, J.D. will continue to fight for our Constitution, stand with our Troops, and will do everything he can to help me MAKE AMERICA GREAT AGAIN," Trump posted on Truth Social.

The applause was even louder as the 78-year-old ex-president showed up to the convention in person hours later, his ear bandaged after the attempt on his life left him wounded.

He waved at the massed delegates and took his seat without speaking, just two days after surviving the shooting at a rally in Pennsylvania. 

While Trump is increasingly confident of a shock return to the White House -- despite multiple legal problems and two impeachments clouding his first term -- President Joe Biden is reeling from weak polls and Democratic concerns over his health.

In the delegate count in Milwaukee, Eric Trump put his father over the threshold on behalf of the Florida delegation, calling him "the greatest president that ever lived."

Vance will boost support from the right but offers less chance of expanding the ticket's appeal to more moderate voters and women.

The standard-bearer for a new kind of populism that has come to the fore under Trump, Vance is also one of the least experienced VP picks in modern history.

But he embraces the ex-president's isolationist, anti-immigration America First movement and is even further to the right than his new boss on some issues including abortion, where he embraces calls for federal legislation.

He initially made his name with the 2016 memoir "Hillbilly Elegy," a best-selling account of his Appalachian family and modest Rust Belt upbringing that gave a voice to rural, working-class resentment in left-behind America.

Turning his back on previous Republican opposition to Trump, whom he once said might be "America's Hitler," Vance reinvented himself and ultimately won the ex-president's endorsement in the 2022 Ohio Senate race, launching his meteoric rise.

Strong polling

Some 50,000 Republicans descended on the shores of Lake Michigan for the four-day Republican National Convention, four months before election day.

The gathering comes with the country reeling from a botched attempt by a gunman to kill Trump at a rally in Butler, western Pennsylvania on Saturday.

The attack -- which killed one bystander and left Trump with a bloodied ear -- was expected to dominate proceedings. 

Leading in multiple polls, despite being convicted at his hush-money criminal case in New York, Trump is exuding confidence.

At 81, Biden meanwhile is facing calls from his own side to quit the race over concerns around his age. 

His campaign released a statement saying the Trump-Vance agenda would "take away Americans' rights, hurt the middle class, and make life more expensive -- all while benefiting the ultra-rich and greedy corporations."

Message of unity

Trump told the New York Post he had "prepared an extremely tough speech" about Biden's "horrible administration" to deliver at the convention.

As some Republicans -- including Vance -- sought to blame Democrats' anti-Trump rhetoric for the attack, Trump also said he hopes to "unite our country."

Still, that means him having to rein in the instinct to settle scores -- demonstrated by his cry for supporters to "fight" in the seconds after Saturday's attack.

The Milwaukee gathering is largely designed in Trump's image, with digital banners beaming out a message in the cavernous convention arena: "Make America Great Once Again."

The branding reflects his takeover of the party.

A diminished figure after his 2020 election loss and a subsequent riot at the Capitol by his supporters, Trump has spent much of the last four years reshaping Republican politics.

Installing loyalists including his daughter-in-law Lara Trump atop the Republican National Committee, the billionaire has effectively crushed dissent within the party.

He scored another victory Monday as a judge dismissed one of the criminal cases against him, concerning accusations he endangered national security by holding on to top secret documents after leaving the White House.