Trump, 78, was holding a campaign rally on Saturday in Butler, Pennsylvania - a key state in the November 5 election - when a 20-year-old man with an AR-15-style rifle got close enough to shoot at the former Republican president from a rooftop.
One shot hit Trump's upper right ear, leaving his face streaked with blood, but he was not severely wounded. His campaign said he was doing fine.
"That reality is just setting in," Trump told the Washington Examiner.
"I rarely look away from the crowd. Had I not done that in that moment, well, we would not be talking today, would we?"
Trump said it was either "by luck or by God" that he survived.
"I'm not supposed to be here. I'm supposed to be dead," he told the New York Post during the same interview.
One person in the crowd was killed and two others wounded before Secret Service agents fatally shot the gunman.
Donald Trump was rushed off stage by secret service agents, after the shooting in Pennsylvania. (AP PHOTO)
On Sunday Trump and US President Joe Biden counselled calm and unity, aiming to lower temperatures in a country whose a deep political divide has grown even more pronounced during the presidential race.
Trump pumped his fist in the air several times as he descended the stairs from his plane after arriving in Milwaukee, where he will accept his party's formal nomination at the Republican National Convention with a speech on Thursday.
"This is a chance to bring the whole country, even the whole world, together. The speech will be a lot different, a lot different than it would've been two days ago," Trump told the Washington Examiner.
"I want to try to unite our country," he told the New York Post during the flight to Milwaukee. "But I don't know if that's possible. People are very divided."
The FBI identified Thomas Matthew Crooks of Bethel Park, Pennsylvania, as the suspect in what it called an attempted assassination. He was a registered Republican, according to state voter records and had made a $US15 donation to a Democratic political action committee at the age of 17.
FBI officials said on Sunday the shooter acted alone. The agency said it had yet to identify an ideology linked to the suspect or any indications of mental health issues or found any threatening language on the suspect's social media accounts.
Biden, a Democrat, ordered a review of how the gunman, who was shot dead by agents moments after opening fire, could have taken up an elevated position so close to Trump, who as a former president has lifetime protection by the US Secret Service.
Biden said the assassination attempt on Trump was "contrary to everything we stand for as a nation".
"There is no place in America for this kind of violence," he said at the White House.
US President Joe Biden called for calm and unity during an address from the Oval Office. (AP PHOTO)
Trump is due to receive his party's formal nomination at the Republican National Convention, which kicks off in Milwaukee on Monday.
Republican National Convention Chairman Michael Whatley said on Fox News that authorities are working together to safeguard the venue, where officials have spent months making security preparations.
The Secret Service denied accusations by some Trump supporters that it had rejected campaign requests for additional security.
"The assertion that a member of the former president's security team requested additional security resources that the US Secret Service or the Department of Homeland Security rebuffed is absolutely false," Secret Service spokesperson Anthony Guglielmi said in a statement.
"In fact, recently the US Secret Service added protective resources and capabilities to the former president's security detail."
While mass shootings at schools, nightclubs and other public places are a regular feature of American life, the attack was the first shooting of a US president or major party candidate since the 1981 attempted assassination of Republican President Ronald Reagan.
with DPA
