Jeremy Clarkson also accused the prime minister of lying to the public
Top Gear presenter Jeremy Clarkson has said he is sorry for calling Gordon Brown a "one-eyed Scottish idiot".
He said: "In the heat of the moment I made a remark about the Prime Minister's personal appearance for which, upon reflection, I apologise."
The broadcaster made the comments to journalists in Sydney when he was speaking about the economic crisis.
The Royal National Institute for the Blind said it had offered to meet Mr Clarkson to discuss his comments.
Clarkson later clarified his apology, telling The Sun that he "very specifically apologised for making fun of his personal appearance - very specifically. I haven't apologised for calling him an idiot."
The BBC said it noted Clarkson's apology for the comments and would be taking no further action.
Public figures have reacted angrily to the presenter's remarks, with Labour MP Gordon Banks saying what Clarkson said was "unforgivable".
Number 10 would only say that Clarkson "is entitled to his own interpretation of the economic circumstances".
The spokesperson declined to comment on the specific insult about Mr Brown, who lost the sight in one eye after an accident as a teenager.
But the Royal National Institute for Blind People called the comment offensive.
"Any suggestion that equates disability with incompetence is totally unacceptable," said chief executive Lesley-Anne Alexander.
"Our offer is still open for Mr Clarkson to talk to us and learn more about the real contribution people with sight loss make to all aspects of society."
Scottish Labour leader Iain Gray joined in the criticism.
"Such a comment is really a reflection on Jeremy Clarkson and speaks for itself," he said.
"Most people here are proud that the prime minister is a Scot and believe him to be the right person to get the UK through this global economic crisis."
Clarkson is in Australia to host Top Gear Live, a stage version of the hit BBC show.
The controversial presenter compared Mr Brown to Australian Prime Minister Kevin Rudd, shortly after Mr Rudd had addressed the country on the severity of the global financial crisis.
Clarkson said: "He [Rudd] genuinely looked terrified. The poor man, he's actually seen the books.
"In England we have this one-eyed Scottish idiot... he keeps telling us everything's fine and he's saved the world and we know he's lying, but he's smooth at telling us."
It had also been reported that Clarkson had called Australians "apes". However the BBC press office has strongly denied that this was the case.
They said that the presenter was referring to some of the UK audience members, in keeping with the style of the programme.
"Top Gear is known for its tone - the presenters take the mickey out of each other, and the Top Gear studio audience aren't immune from that either."
Former BBC director General Greg Dyke said he did not believe Clarkson should be taken off air.
"The truth is if Jeremy Clarkson worked in news or current affairs he would be fired, he would be out of there because you can't have anybody who is supposed to be impartial making that kind of statement.
"Clarkson's Clarkson, he says many things that I find deeply offensive quite regularly. I think that's life - I think if you take all those people out of the media and off television you get a very boring media."
In November, more than 1,800 people complained to the BBC after Clarkson made a joke on Top Gear about lorry drivers killing sex workers.
The joke followed the conviction of forklift truck driver Steve Wright for the murders of five prostitutes in Ipswich.
Some 340 people also complained to regulator Ofcom, but it later ruled the joke did not breach the broadcasting code.