Biden tells Americans to 'cool it down' in Oval Office address after Trump assassination bid

US President Joe Biden sought to calm a divided nation Sunday after his rival Donald Trump survived an assassination bid, saying in a rare Oval Office address that it was time to lower the temperature of America's hostile politics.

"It's time to cool it down. We all have a responsibility to do that," Biden said in a televised address following the attack in which Republican Trump was injured in the ear and a bystander was killed by gunfire.

As the country reeled from images of a bloodied Trump waving his fist after the gunman opened fire at a campaign rally in Pennsylvania, Biden added that US politics "must never be a literal battlefield, God forbid a killing field."

The 20-year-old shooter, Thomas Matthew Crooks, was shot dead by Secret Service agents amid scenes of chaos. Authorities say his motive remains unclear.

The FBI said it was investigating the attack as a potential act of domestic terrorism and studying Crooks's phone to discover any "ideologies" he may have had.

Biden, giving just the third Oval Office address of his presidency, also mentioned the January 6, 2021, Capitol attack by pro-Trump supporters as proof that the situation is getting out of hand.

"We can't allow this violence to be normalised," the 81-year-old Democrat said, adding that the November 5 election would be a "time of testing" for the United States.

The short but forceful speech went without any major hitches, bar Biden twice referring to the ballot box as a "battle box". Democrats are closely watching the president following a disastrous debate performance, which renewed concerns about his age and ability to govern.

The attempt on Trump's life has opened a dark new chapter in an already polarised election rematch with Biden, who beat him in 2020.

Despite their bitter enmity, both Biden and Trump called for calm after the most serious attack on a US president or ex-president in more than four decades.

Trump said it was "more important than ever that we stand united" and added that Americans should not allow "evil to win," in a post on social media.

Numerous Republicans – who themselves often pose with guns in political ads – have claimed Democrats have promoted extreme rhetoric that led to the shooting.

Just before Biden's speech, Trump landed in Milwaukee for the Republican National Convention, during which he will formally be anointed the party's nominee.

The US Secret Service insisted the agency is "fully prepared" to maintain security at the convention, as it comes under severe scrutiny over the attempt to kill Trump.

The agency faces searching questions about how the shooter was able to climb onto a rooftop around 150 metres (500 feet) from where Trump was speaking and fire multiple rounds.

The FBI was "looking at it as a potential domestic terrorism act," the bureau's assistant director of counterterrorism Robert Wells said.

The shooter's father was believed to have bought the semi-automatic weapon used in the attack but it was unclear how the shooter accessed it. Investigators also found a "suspicious device" in the shooter's car.

Crooks's former schoolmates described him as a quiet student who often came across as lonely.

"He was quiet but he was just bullied. He was bullied so much," Jason Kohler, who said he attended the same high school as Crooks, told reporters.

The attack threatens to further inflame tensions at an already febrile moment in the race for the White House.