The cabinet Minister said Clarkson’s apologetic explanation that he had tried not to utter the n-word should be enough to draw a line under the controversy.
But David Cameron’s official spokesman said the Prime Minister believed his friend’s fate was a matter for the broadcaster.
Clarkson became embroiled in the row following claims that he used the n-word while reciting the nursery rhyme Eeny, Meeny, Miny Moe while shooting an episode of the BBC2 programme.
In the footage Clarkson is using the nursery rhyme to compare two sports cars. He said he “mumbled where the offensive word would normally occur” in two takes, and used the word “teacher” in its place in a third.
Last night he posted a video in which he said he “did everything in my power to not use that word” and was now “begging your forgiveness for the fact that obviously my efforts weren’t quite good enough”.
Asked if he backed calls for Clarkson, well known for courting such controversy, to be axed, Mr Gove told ITV’s Good Morning Britain: “No, I don’t.
“The word in question is horrendous and shouldn’t be used but I have read Jeremy Clarkson’s account in the papers today, his explanation, and it seems to me that this was a word that he never intended to utter, never intended to broadcast. He has been clear in his apology and I think we should leave matters there.”
Asked if the PM shared his colleague’s opinion, Mr Cameron’s official spokesman said: “He does share the Education Secretary’s view: It is absolutely right that there has been an apology.”
Clarkson said: “I wish to God that my attempts to cover up that word were better than they were.
“I was simply mumbling – saying ‘ner ner’ or something similar, anything but the n-word. It was my mistake and I apologise for not covering it up. But if you look at the footage you can see what I’m trying to do.”
The BBC said it had “left him in no doubt about how seriously we view this”.