State voter records show Crooks was a registered Republican, US media report. He also reportedly donated $15 to a liberal campaign group in 2021.
The Republican presidential candidate had just started addressing his supporters in Butler, Pennsylvania – a crucial swing state in November’s election – when the shots started.
Multiple bangs rang out as Trump spoke about his successor, President Joe Biden, and his administration.
Several supporters holding placards and standing behind Trump ducked as the shots were heard.
Bystanders who spoke to the BBC suggested the gunshots may have come from a one-storey building to the right of the stage where Trump was speaking.
One witness – Greg – told the BBC that he had spotted a suspicious-looking person “bear crawling” on the roof of the building about five minutes after Trump took to the stage. He said he pointed the person out to police.
“He had a rifle, we could clearly see him with a rifle,” he said. “We’re pointing at him, the police are down there running around on the ground – we’re like ‘hey man there’s a guy on the roof with a rifle’ and the police did not know what was going on.”
Tim – who was also at the rally – told the BBC that he had heard a “barrage” of shots.
“There was a spray which we initially thought was a fire hose, and then the speaker on the right-hand side started coming down,” he said.
“Something must have hit the hydraulic lines [which caused it to fall]. We saw President Trump go to the ground and everyone started dropping to the ground because it was chaos.”
Warren and Debbie were at the venue and told the BBC they heard at least four gunshots.
They said they both got on the ground as Secret Service agents came through the crowd, shouting for the attendees to get down. People remained calm, they said.
“We couldn’t believe it was happening,” Warren said.
Debbie said a little girl beside them was crying that she didn’t want to die and saying “how is this happening to us?”
“That broke my heart,” Debbie said.
Republican Congressman Ronnie Jackson told the BBC that his nephew was injured in the shooting. He sustained a minor wound to his neck and was treated at the scene, Mr Jackson said in a statement.
Speaking from his home state of Delaware, President Biden deplored the attack, calling it “sick”.
“There’s no place in America for this kind of violence,” he said. “Everybody must condemn it.”
The White House later said President Biden had spoken with Trump before returning to Washington DC.
Trump remains locked in a tight contest with President Biden – the presumptive Democratic nominee – in a re-match of the 2020 election.
Politicians of both parties joined Mr Biden in condemning the apparent attack.
Former President Barack Obama said there “is absolutely no place for political violence in our democracy” and that he was “relieved that former President Trump wasn’t seriously hurt”.
Trump’s former vice-president Mike Pence said he and his wife were praying for his former ally, adding that he urged “every American to join us”.
House Minority Leader Hakeem Jeffries said in a statement: “My thoughts and prayers are with former President Trump. I am thankful for the decisive law enforcement response. America is a democracy. Political violence of any kind is never acceptable.”
UK Prime Minister Sir Keir Starmer led international condemnation of the shooting, saying he was “appalled by the shocking scenes at President Trump’s rally”.
“Political violence in any form has no place in our societies and my thoughts are with all the victims of this attack,” he said in a statement.
Trump is still set to accept his party’s nomination for president at the convention in Milwaukee on Monday, his campaign managers said. Some had speculated that he had been set to reveal his running mate at the Butler rally.
Some Republicans were quick to blame President Biden over the shooting, accusing him of stoking fears about Trump’s potential return to office.
Senator JD Vance, who is thought to be on the shortlist to become Trump’s vice-presidential candidate, said the rhetoric from the Biden campaign had led directly to this incident.
Mike Collins – a Republican congressman – accused the president of “inciting an assassination”.
Meanwhile James Comer, the chair of the powerful House oversight committee, said he would summon the director of the Secret Service before his panel.