The Pirates of the Caribbean star spoke during an appearance at the Glastonbury music festival, pondering how long it had been since an actor had killed a US president.
His remarks drew rebukes from supporters of Mr Trump, and the White House described Depp's remarks as “sad.”
Depp has his remarks were not intended maliciously.
"I apologise for the bad joke I attempted last night in poor taste about President Trump," Depp, 54, said in a statement.
"It did not come out as intended, and I intended no malice. I was only trying to amuse, not to harm anyone."
Depp was at a screening of his 2004 film “The Libertine” at the Glastonbury festival when discussion turned to the topic of Trump. Depp said he thought the president “needs help.”
“Can we bring Trump here?” Depp asked the audience. “... When was the last time an actor assassinated a president?”
Actor John Wilkes Booth assassinated US President Abraham Lincoln in 1865.
“Now I want to clarify, I'm not an actor,” Depp continued. “I lie for a living. However, it's been a while, and maybe it's time.”
White House Press Secretary Sean Spicer described the remarks as "troubling" in a press briefing.
Earlier the White House said in a statement: “President Trump has condemned violence in all forms and it's sad that others like Johnny Depp have not followed his lead”.
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“I hope that some of Mr. Depp's colleagues will speak out against this type of rhetoric as strongly as they would if his comments were directed to a Democratic elected official.”
The US Secret Service said it was aware of Depp's comments but had no other comment.
Some Republicans criticised Depp's comments as part of a grim trend.
“I'm sick of celebrities getting away with such disgusting comments,” Ronna Romney McDaniel, the Republican National Committees chairwoman, wrote on Twitter.
Earlier in June, Delta Air Lines and Bank of America pulled their sponsorship of a New York production of Shakespeare's Julius Caesar because the assassinated Roman ruler was portrayed as a Trump-like businessman.
Last month comedian Kathy Griffin posed in photographs holding up a fake bloody, severed head resembling Trump. She also apologized but was fired from hosting CNN's annual New Year's Eve broadcast.
Last week, a gunman opened fire on Republican legislators in who were practising for a charity baseball game.
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