The Republican presidential nominee, at an event in Flint, Michigan, described running for president as "a dangerous business" akin to car racing or bull riding.
"Only consequential presidents get shot at," he said.
Earlier, vice president Kamala Harris struck a measured tone, even steering clear of mentioning Trump by name in an interview with black journalists that starkly contrasted with the former president's own highly contentious appearance before the same group.
Democratic presidential nominee Kamala Harris spoke with Trump in a phone call. (AP PHOTO)
The two candidates briefly put their differences aside in a phone call Trump described as "very, very nice" even as crowds booed when he mentioned Harris by her first name.
Harris said earlier in the day that she told Trump "there's no place for political violence in our country".
Both sides are ramping up campaigning with no changes to Trump's calendar despite the apparent assassination attempt at one of his Florida golf courses, which has renewed accusations by Republicans that Democrats' criticism against Trump is inspiring violent attacks.
Democrats have accused Trump in the past for his long history of inflammatory campaign rhetoric and advocacy for jailing or prosecuting his political enemies. But Harris was treading more carefully in the aftermath of the latest incident.
Her session with the National Association of Black Journalists (NABJ) was one of the few extensive sit-down interviews she has done since replacing President Joe Biden on the Democratic ticket in July.
She repeatedly criticised Trump on issues including his handling of the COVID-19 pandemic and opposition to abortion access, but was careful to refer to him as the former president and in other ways that avoided naming him directly.
We must pass a law to restore reproductive freedom. — Kamala Harris (@KamalaHarris) When I am President of the United States, I will proudly sign it into law. Lives depend on it.September 18, 2024
Harris answered questions from three association journalists at a small, relatively quiet venue at the Philadelphia studios of public radio station WHYY.
That was very different from Trump addressing the NABJ conference in Chicago in July, when he was antagonistic to the moderators and sparked an uproar by questioning the vice president's racial identity.
Her manner was a departure from her campaign rallies, where Harris often receives some of her loudest applause by declaring that her professional background as a prosecutor means "I know Donald Trump's type".
Pressed about reports of eroding support among black male voters, Harris said she was not "assuming I'm gonna have it because I'm black".
She ducked a question about whether she would support efforts by some congressional Democrats for reparations from the government to compensate descendants of slaves for years of unpaid labour by their ancestors. Biden has backed the idea of at least studying reparations.
So far, Biden and Harris have tried to avoid politics in their responses to Sunday's incident, instead condemning political violence of all kinds. The president also urged Congress to increase funding to the Secret Service.
Ryan Wesley Routh is the suspect in the apparent assassination attempt on Trump. (AP PHOTO)
Trump has claimed, without evidence, that months of criticism against him by Harris and Biden, who call him a threat to American democracy, inspired the latest attack.
Authorities say Ryan Wesley Routh camped outside the golf course in West Palm Beach, where Trump was playing on Sunday, for nearly 12 hours with food and a rifle but fled without firing shots when a Secret Service agent spotted and shot at him. He was subsequently arrested as he drove away.
Routh has two prior convictions, both in North Carolina, according to the criminal complaint: a 2002 conviction for possession of a weapon of mass death and destruction and a 2010 conviction for possession of stolen goods.
