Charles and Queen Camilla are due to arrive in America for a four-day state visit, but questions arose after a man opened fire on security personnel near the White House Correspondents' Association dinner on Saturday, local time.
"I think it's great; he'll be very safe," Trump said in an interview on CBS. "The White House grounds are really safe."
Trump also said there was no indication from authorities that there were additional threats to himself or other officials.
US authorities believe the shooting likely targeted the president and administration officials, acting US Attorney General Todd Blanche said.
Blanche also said he was confident Charles would be safe during this week's visit to the US, which kicks off on Monday, local time.
The four-day trip - which is to include a private meeting with Trump and an address to Congress marking 250 years since US independence - is intended to reinforce the strained US-British relationship amid differences over the Iran war.
"Following discussions on both sides of the Atlantic through the day, and acting on advice of government, we can confirm the state visit by their majesties will proceed as planned," a Buckingham Palace spokesperson said.
"The King and Queen are most grateful to all those who have worked at pace to ensure this remains the case and are looking forward to the visit getting under way tomorrow."
A palace source said there might be small operational changes to one or two engagements.
Earlier, the spokesperson said Charles was being kept fully informed of developments and was relieved that Trump, his wife and all guests had been unharmed.
Charles and Camilla have also privately reached out to Trump and first lady Melania Trump to express their sympathies, a palace source said.
British senior minister Darren Jones said the government would continue to co-operate closely with US security services ahead of Charles' visit and extensive discussions already under way would continue in the coming days.
"In respect of His Majesty's visit to the United States next week ... our security services obviously remain in close co-operation in advance of that," Jones told Sky News.
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