The author said in a since-deleted post on Twitter that he thinks of a "rope" and "the nearest lamp-post" when he hears Mr Johnson's name.
After being met with a backlash on Thursday, Sir Philip said he had made a "tactical error", but refused to apologise for his anger at the Prime Minister's decision to suspend Parliament.
Following criticism online, the Northern Lights author blamed recent political events for his post and said he wanted to make it "perfectly clear" that he did not want to kill the Prime Minister.
On Wednesday, Mr Johnson said he wanted to prorogue Parliament in order to bring the current record-breaking session to a close and work on his Government's new legislative agenda.
The decision provoked strong reactions, with opposition leaders accusing the Prime Minister of trying to halt their efforts to block a no-deal Brexit.
In a string of tweets, Sir Philip, 72, wrote: "I've deleted a tweet which apparently upset a lot of people. I don't advocate hanging Boris Johnson. I think that would be a very bad idea."
"Recent events have aroused my anger to the point where I temporarily lost my judgement. In the heat of the moment I made a tactical error.
"Johnson's attempt to silence Parliament is a low point in our nation's political history. It was not my aim to distract from the genuine and legitimate outrage of many people at this, and I'm sorry it happened.
"Freedom of speech, like freedom of assembly, is precious. So is life.
"Just to make it perfectly clear: I wouldn't kill the prime minister, and I don't want anyone else to. But I don't apologise for the anger I feel; only for its intemperate expression."
Alongside a screenshot of the deleted tweet, Mr Courts said: "The voice of reasonable, tolerant debate from @PhilipPullman. He's deleted his tweet, but here's what he said.
"You always know people have lost the argument & have little intellectual confidence in their case when they resort to hideous language & sick personal abuse like this."
Sir Philip's latest controversial tweets follow a post on Wednesday which called the Prime Minister a dictator, adding: "We must get rid of him and his loathsome gang as soon and as finally as possible."