Washington DC - Rivals Joe Biden and Donald Trump urged Americans to show unity Sunday after an assassination attempt on the Republican put the nation on edge in the run-up to the presidential election.

President Biden said he would address the nation from the Oval Office later in the day, a step only taken at times of grave crisis after his 78-year-old predecessor was hit in the ear at a campaign rally in Butler, Pennsylvania.

"Unity is the most elusive goal of all, but nothing is more important than that right now," Biden said in brief remarks from the White House, flanked by Vice President Kamala Harris and his homeland security chief.

The 81-year-old Democrat said he had a "short but good conversation" on Saturday with Trump, his political nemesis whom he regularly brands as a threat to democracy.

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Biden said the motives of the shooter, 20-year-old Thomas Matthew Crooks, remained unknown and urged people not to make assumptions about his "afflations."

A day after being rushed from the stage by Secret Service agents with blood streaked across his face, Trump made a similar call.

"In this moment, it is more important than ever that we stand United," Trump said in a statement on his Truth Social network, adding that Americans should not allow "Evil to win."

The tycoon added that it was "God alone who prevented the unthinkable from happening" and that he would "FEAR NOT."

Secret Service snipers killed Crooks after he fired multiple shots at the rally from a nearby rooftop. A bystander was killed and two spectators critically injured in the worst act of US political violence in decades.

Biden said he had ordered a full review of security at the rally, as well as at this week's Republican National Convention in Milwaukee, where Trump will be crowned the party's presidential nominee.

Biden also praised the victim, named Corey Comperatore, saying he "was protecting his family from the bullets."

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Questions are swirling about the motive of shooter Crooks, whose body was seen in television images on a low roof of a building near a weapon understood to have been an AR-15-style semiautomatic rifle.

Investigators had found explosive material in his car parked near the scene, US media said, while the FBI also searched his house. The shooter, reportedly a registered Republican, was believed to be working alone.

His father, Matthew Crooks, told CNN that he was trying to establish "what the hell is going on."

The shocking incident also drew criticism of security at the rally, particularly about how a presidential candidate could be targeted by a gunman around 500 feet away despite a huge Secret Service detail.

Secret Service spokesman Anthony Guglielmi rejected "absolutely false" claims that it had refused additional protection for Trump ahead of the rally.