Pressure is growing to increase the Secret Service protection provided to Donald Trump after the second assassination attempt on the former president in just over two months.
"The Service needs more help," President Biden told reporters at the White House on Monday.
"And I think that Congress should respond to their needs if they in fact need more service people," he said. "They're deciding whether they need more personnel or not."
Ryan Wesley Routh, the alleged gunman, faced federal gun counts at a Florida court on Monday, though he could face more serious charges when prosecutors go to a grand jury for an indictment.
In an interview with Fox News, Trump blamed President Biden and Vice-President Harris for the attack.
"He believed the rhetoric of Biden and Harris, and he acted on it," Trump told Fox News.
"Their rhetoric is causing me to be shot at," he said, "when I am the one who is going to save the country, and they are the ones that are destroying the country - both from the inside and out."
Both Mr Biden and Ms Harris condemned the incident.
In a statement after the assassination attempt on Sunday, Biden described himself as "relieved" that Trump was unharmed and said: "I have directed my team to continue to ensure that Secret Service has every resource, capability and protective measure necessary to ensure the former President’s continued safety."
Vice-President Harris said in a statement she was "deeply disturbed" by the attempted assassination and that she was "thankful that former President Trump is safe".
"We all must do our part to ensure that this incident does not lead to more violence," she said.
Former Secret Service agents have suggested to the BBC that Trump needs more protection than other former presidents, given that he is running for the White House.
"We now have to re-evaluate," said former agent Barry Donadio. "Should all these candidates get the same presidential protective package? I think that's probably going to have to be the answer."
Speaking to BBC Radio 4's Today programme, a former senior member of the Secret Service, Robert McDonald, agreed that the agency had a "good day" despite Trump's would-be assailant getting relatively close to the former president.
The assassination attempt in Pennsylvania in July led to the resignation of Kimberly Cheatle, the Secret Service chief who admitted that the agency had had its "most significant operational failure" in decades.
Her replacement, Ronald Rowe, is on his way to Florida, according to US media.
Several members of Congress, from both major parties, have said that presidential candidates should receive the same level of protection as the sitting president.
Routh was allegedly able to get within about 300-500 yards (275-460m) of Trump while carrying an SKS-style rifle.
Palm Beach County Sheriff Ric Bradshaw has pointed out that Trump does not receive the same level of protection that a sitting president does.
"If he was, we would have had this entire golf course surrounded," he said.
Authorities have charged Routh with possession of a firearm as a convicted felon and possession of a firearm with an obliterated serial number. He will attend another next week to determine whether he should remain in custody.
Trump told supporters that he was safe and well, and thanked the Secret Service - the government agency with responsibility for protecting the president and major US officials - and other law enforcement agencies for doing an "incredible job".
But politicians from both parties have called for increased security around the former president.
“It is inexplicable that this happened again,” Representative Claudia Tenney of New York, a Republican, posted on X. “President Trump needs the same, if not more, Secret Service protection than a sitting President.”
A number of Democrats also called for a review of security procedures.
“Two assassination attempts in 60 days on a former President & the Republican nominee is unacceptable,” tweeted Ro Khanna, a Democratic member of the House from California.
“The Secret Service must come to Congress tomorrow, tell us what resources are needed to expand the protective perimeter, & lets allocate it in a bipartisan vote the same day.”