Authorities used the gun to help determine the shooter's identity, as he did not have identification on him, according to law enforcement sources, as reported by CNN.
This comes amid ongoing probes by lawmakers and an internal government watchdog into how the agency handled Trump's safety and how a gunman nearly killed the Republican presidential candidate for Pennsylvania during a rally this month.
He lived in the Pittsburgh suburb of Bethel Park, about 56 km south of the Trump rally site where law enforcement officials said he fired at Trump, the presumptive presidential candidate of the Republican Party.
Reacting to the FBI's statement, Trump told his supporters that he has accepted an apology from the FBI.
Thomas Matthew Cooks was planted on the roof of a manufacturing plant located over 130 yards away from the stage at Butler Farm Show grounds, the New York Post reported, citing sources.
The shooter, as per FBI, used an AR-style rifle chambered in 5.56mm, a common calibre for such weapons.
Trump also said he appreciated the call he received from President Joe Biden, also expected to be his rival in the election, according to the Post, calling it "fine" and "very nice."
Two witnesses at Donald Trump's election rally in Pennsylvania, where he was attacked, claimed to have seen the shooter, with one recalling how the gunman moved from roof to roof, apparently scouting for a perfect perch to shoot at the former US president.
Melania reflected on what the incident means for her and her family while calling for the country to "ascend above the hate".
Former United States president Donald Trump was injured after being shot in the ear during an apparent assassination attempt at an election rally in Pennsylvania after which a male attacker was shot and killed by a member of the Secret Service.
When the IAF veterans' bail petition came up for hearing, in an unprecedented move, senior serving and retired Air Marshals and Air Vice Marshals rallied behind the accused officers and appeared before the court to give sureties for each, something that has never happened ever before.
The finance ministry on Friday indicated it will not intervene in the foreign exchange market even if capital inflows into the country touches $50 billion during the 2010-11 fiscal.