Mr Crooks, 20, was shot dead after he shot at the Republican presidential nominee during a rally in Pennsylvania on Saturday. One other rally attendant was shot dead while two others were severely injured from the shootings.
The FBI has now described the attack as an assassination attempt on Mr Trump, saying the gunman fired multiple shots, CNN reports.
Mr Trump was briefly treated at the hospital after the incident with the former president saying he was shot at the “upper part of my right ear.”
However, the attack has been condemned by Mr Trump’s main opponent, President Joe Biden, and ex-President Barack Obama.
Mr Biden, who was in Delaware during the shooting, has also spoken to Mr Trump, the White House said.
In his reaction, former President Obama wrote on X that there “is absolutely no place for political violence in our democracy.” He said he was “relieved that former President Trump wasn’t seriously hurt.”
It is unclear how the shooting will impact the November US presidential election that sees Mr Trump locked in a close race with Mr Biden of the Democratic Party.
Mr Trump, 78, is popular among conservatives and right-wing voters and has repeatedly campaigned against immigration and vowed to deport thousands of illegal immigrants.
Mr Biden, 81, who is currently the Democratic Party candidate, supports a more inclusive society and has created pathways for illegal immigrants without crime records to become American citizens. He faces internal criticism from his party following concerns about his cognitive ability, especially after a poor debate performance against Mr Trump. Although there have been calls from some Democrats that he should drop from the race, the president has said he would not and would defeat Mr Trump in the election.
It will be recalled that Donald Trump survived a weekend assassination attempt days before he is due to accept the formal Republican presidential nomination, in an attack that will further inflame the U.S. political divide and has raised questions about the security lapses.
Trump, 78, had just begun a campaign speech in Butler, Pennsylvania, about 30 miles (50 km) north of Pittsburgh, on Saturday when shots rang out, hitting the former president’s right ear and streaking his face with blood.
“Fight! Fight! Fight!” Trump mouthed to supporters, pumping his fist, as Secret Service agents rushed him away. His campaign said he was doing well and appeared to have suffered no major injury besides a wound on his upper right ear.
The shooting occurred less than four months before the Nov. 5 election, when Trump faces an election rematch with Democratic President Joe Biden. Most opinion polls including those by Reuters/Ipsos show the two locked in a close contest.
One person who attended the rally was killed and two other spectators were critically wounded, the Secret Service said.
“In this moment, it is more important than ever that we stand United, and show our True Character as Americans, remaining Strong and Determined, and not allowing Evil to Win,” Trump said on his Truth Social service on Sunday.
Trump left the Butler area under Secret Service protection and later arrived at his golf club in Bedminster, New Jersey.
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,” said Secret Service spokesperson Anthony Guglielmi in a statement. “In fact, recently the U.S. Secret Service added protective resources and capabilities to the former President’s security detail.”
While mass shootings are a regular feature of American life, the attack was the first shooting of a U.S. president or major party candidate since the 1981 attempted assassination of Republican President Ronald Reagan.
In 2011, Democratic then-Congresswoman Gabby Giffords was seriously wounded in an attack on a gathering of constituents in Arizona. Republican U.S. Representative Steve Scalise was also badly wounded in a politically motivated 2017 attack on a group of Republican representatives practicing for a charity baseball game.
Giffords later founded a leading gun control organization, Scalise has remained a stalwart defender of gun rights.
The attack heightened longstanding worries that political violence could erupt during the presidential campaign and after the election. The concerns in part reflect the electorate’s polarization, with the country appearing bitterly divided into two camps with divergent political and social visions.
Americans fear rising political violence, recent Reuters/Ipsos polling shows, with two out of three respondents to a May survey saying they worried violence could follow the election.
Trump supporters stormed the U.S. Capitol on Jan. 6, 2021, in an attempt to overturn his election defeat, fueled by his false claims that his loss was the result of widespread fraud. More than 100 police officers were injured, five people died and the Capitol suffered millions of dollars of damage in the violence.
Meanwhile, Donald Trump, former US president, has said that he is “doing well” after gunshots were fired at his rally in Pennsylvania, a statement published by the Republican National Committee (RNC) said.
Before the shooting on Saturday, Trump was delivering a speech about how “the worst president in the history of our country took over” and set the US in regression.
Midway into his speech, gunshots rang out in the crowd.
Trump’s security rushed him off the stage but the former US president paused to pump his fist defiantly in the air.
Later, the Republican Party presidential candidate posted a statement on Truth Social, a platform he founded, thanking law enforcement officers and the secret service for their “rapid response”.
“I was shot with a bullet that pierced the upper part of my right ear,” he said.
“I knew immediately that something was wrong in that I heard a whizzing sound, shots, and immediately felt the bullet ripping through the skin.
“Most importantly, I want to extend my condolences to the family of the person at the rally who was killed, and also to the family of another person that was badly injured. It is incredible that such an act can take place in our country.”