Depp said the remark was in "poor taste" and did not "come out as intended", Depp told people.com.
"I apologise for the bad joke I attempted last night in poor taste about President Trump. It did not come out as intended, and I intended no malice. I was only trying to amuse, not to harm anyone," Depp said on Friday.
The clamour led Depp to apologise after his remarks at the Glastonbury festival did not go in the good books of Trump supporters and the White House.
He asked: "Can you bring Trump here?"
After receiving jeers from the crowd, he added: "You misunderstand completely. When was the last time an actor assassinated a president? "I want to clarify. I'm not an actor. I lie for a living but it's been a while. Maybe it's about time. I think he needs help and there are a lot of wonderful dark, dark places he could go," he said.
Trump supporters condemned the actor and the White House described his comments as "sad".
Depp's remarks on Thursday came as he introduced a screening of his film "The Libertine" at the festival in south-west England.