In what could be a reference to Abraham Lincoln's murder by actor John Wilkes Booth in 1865, Depp said, "When was the last time an actor assassinated a president?"
"I want to qualify, I am not an actor. I lie for a living. However, it has been a while and maybe it is time," the actor added.
Depp, 54, was at the Glastonbury music festival when he made the remarks.
He attended the festival to introduce his 2004 film "The Libertine" along with director Julian Temple but began talking about the 45th US president, reported The Guardian.
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The actor was aware that his remarks would cause controversy as he said, "It is just a question - I'm not insinuating anything. By the way, this is going to be in the press. It will be horrible."
Depp's comments have met with criticism with some on social media suggesting a boycott of his movies.
"I would call for a boycott of Johnny Depp's movies, but it appears people have been avoiding them for the last 20 years anyway," a user wrote.
"No joke about killing @POTUS is acceptable. I'm sick of celebrities getting away with such disgusting comments," tweeted politician Ronna Romney McDaniel.
Trump's son Donald Trump Jr mocked the actor by posting a link of a story about Heard's abuse allegations.
"Ha, Depp wants to make social commentary: Johnny Depp's team knew of alleged abuse of Amber Heard," he wrote with the links to the story.
"Johnny Depp was joking people... That means it is not serious, stop being such snowflakes. It shouldn't even be a story," a Twitter user wrote.
Depp is not the first celebrity to have made violent comments against Trump as comedian Kathy Griffin recently came under fire for posing with what seemed to be a severed head of the president. She was fired by CNN from hosting a show after the controversy.
Early this year, Madonna, speaking at the Women's March on Washington, had said that she thought about "blowing up the White House."
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