"The Pirates of the Caribbean" star spoke during an appearance at Britain's Glastonbury music festival on Thursday when he pondered how long it had been since an actor had killed a US president.
"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."
Depp on Friday said his remarks were not intended maliciously.
“I apologize 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.”
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."
The US Secret Service said it was aware of Depp 's comments but had no other comment.
Some Republicans criticized 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.
Depp , whose latest "Pirates of the Caribbean" movie was panned by critics in May, has had more than a year of bad press following an acrimonious divorce from actress Amber Heard and a lawsuit against his former business managers that has detailed claims of lavish spending by the actor.
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 lawmakers in who were practicing for a charity baseball game.