President Joe Biden, said he had ordered a review of how a 20-year-old man carrying an AR-15-style rifle managed on Saturday to get close enough to shoot from a rooftop at Trump, who as a former president has lifetime protection by the U.S. Secret Service, a unit of the federal Department of Homeland Security.
Trump, 78, was holding a Saturday campaign rally in Butler, Pennsylvania - one of the states expected to be most competitive in the November 5 election - when shots rang out, hitting his right ear and streaking his face with blood.
His campaign said he was doing well and appeared to have suffered no major injury besides a wound on his upper right ear.
"Based on yesterday's terrible events, I was going to delay my trip to Wisconsin, and The Republican National Convention, by two days, but have just decided that I cannot allow a "shooter," or potential assassin, to force change to scheduling, or anything else. Therefore, I will be leaving for Milwaukee, as scheduled," Trump wrote on his Truth social media account.
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 $15 donation to a Democratic political action committee at the age of 17.
Law enforcement officials told reporters they had yet to identify a motive for the attack.
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," Biden said at the White House.
"I urge everyone, everyone please don't make assumptions about his motive or affiliations," Biden said.
Trump is due to receive his party's formal nomination at the Republican National Convention, which kicks off in Milwaukee, Wisconsin, on Monday.
Republican National Convention Chairman Michael Whatley said on Fox News on Sunday that authorities are working together to safeguard the venue, where officials have spent months making security preparations.
Authorities identified a rally attendee who was shot and killed as Corey Comperatore, 50, of Sarver, Pennsylvania, who Pennsylvania Governor Josh Shapiro told reporters was killed when he dove on top of his family to protect them from the hail of bullets.
"Corey was an avid supporter of the former president, and was so excited to be there last night with him in the community," Shapiro said.
"Political disagreements can never, ever be addressed through violence."
Two other rally attendees were critically wounded, the Secret Service said.
The Secret Service in a statement 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 U.S. 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 U.S. Secret Service added protective resources and capabilities to the former President's security detail."
The shooting occurred less than four months before the November 5 election, when Trump faces an election rematch with Biden.
Most opinion polls including those by Reuters/Ipsos show the two locked in a close contest.
The shooting whipsawed the discussion around the presidential campaign, which had recently focused on whether Biden, 81, should drop out following a disastrous June debate performance.
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.
