Jeremy Clarkson made light of his suspension by the BBC, as an online petition for him to be reinstated topped 500,000 signatures.
The Top Gear presenter told reporters he was "just off to the jobcentre" as he left his home in London.
Asked if he had any regrets about what had happened, he replied "yes".
The 54-year-old star was suspended on Tuesday following what the BBC said was "a fracas" with producer Oisin Tymon.
Prime Minister David Cameron told the BBC: "I don't know exactly what happened. He's a constituent of mine, a friend of mine. He's a huge talent."
BBC director-general Tony Hall said an investigation was going on to "gather the facts" about the incident.
"We do not have the facts at the moment," he said. "I am a fan of Jeremy Clarkson but this is a serious thing that is alleged to have taken place."
A lawyer for Mr Tymon said his client "intends to await the outcome of the BBC investigation and will make no comment until that investigation is complete".
'Amuses and entertains'
Speaking to BBC One's Midlands Today programme, Mr Cameron said: "Because he is such a huge talent and he amuses and entertains so many people, including my children, who'd be heartbroken if Top Gear was taken off air, I hope this can be sorted out, because it's a great programme and he's a great talent.
"Every organ has to be free to manage its talent. I don't want to interfere in the running of the BBC. I hope it can be sorted out.
"The prime minister has many responsibilities, sadly, securing the future of Top Gear isn't one of them".
Sunday's episode of Top Gear will not be shown, and it is understood the two final episodes in the series will also be dropped.
The online petition in support of Clarkson - set up by political blogger Guido Fawkes - was nearing half a million signatures less than 24 hours after it was launched on Tuesday afternoon.
Earlier, Clarkson's co-presenter James May said: "I think he's been involved in a bit of a dust-up and I don't think it's that serious." He said he had not been present at the alleged incident.
Top Gear is one of the BBC's most popular and profitable TV shows, with Clarkson appearing on it since 1988. The programme has an estimated global audience of 350 million.
Former BBC Trust chairman Sir Michael Lyons said the focus should be on the incident alone, and that the popularity of the show should not influence the corporation's decision.
"There is nobody who is bigger than the BBC's reputation," he said. "This has been a nagging problem for some time. But it must be dealt with on the facts of the moment - not the sort of legacy and it certainly mustn't be clouded by arguments about what the BBC earns.
"I think the BBC's learnt that actually it can replace even the biggest names, even if needs to, and I'm not saying it needs to."
Former culture secretary Maria Miller said the BBC had to improve the way it dealt with "larger than life characters".
"I think they need to sort this mess out quickly, and not be seen to be punishing the fans," she told BBC Radio 4's World at One.
"It's a fantastic show and I really think the BBC has got an obligation to get this sorted."
Earlier on Wednesday, Clarkson had retweeted a message to his 4.5m Twitter followers from a Top Gear viewer which read: "How can BBC not show the remaining episodes of Top Gear, can't this be resolved without making the fans suffer?"
He had also exchanged suggestions on Twitter with Top Gear co-hosts Richard Hammond and May about films that could be aired in place of Sunday's planned episode.
The Daily Mirror said the alleged incident took place after filming in Newcastle over a lack of catering.
Clarkson's suspension was announced in a BBC statement on Tuesday afternoon which said: "Following a fracas with a BBC producer, Jeremy Clarkson has been suspended pending an investigation.
"No one else has been suspended. Top Gear will not be broadcast this Sunday. The BBC will be making no further comment at this time."
What is a 'fracas'?
"Fracas" has French roots but it is originally from the Italian "fracassare", to cause uproar.
Its first noted use in English was in 1727, according to the Oxford English Dictionary. The writer Lady Mary Worley Montagu wrote in a letter: "A… violent fracas took place between the infantry-colonel and his lady."
If you speak British English, you pronounce it "frah-car", but Americans tend to pronounce it "fray-cuss".
Neil Taylor, managing partner of The Writer, a language consultancy business, says use of the word peaked in 1945, and has dropped off since then. "It's a nicely non-specific word," he says, "although you do get the sense of something physical - without anything being confirmed."
Perry McCarthy, the original Top Gear stunt driver The Stig, said he thought the BBC had taken the show off the air too quickly. "Why take the show off air while they look into it? I just think it's a complete overreaction."
Clarkson and his co-presenters are scheduled to appear in four Top Gear Live stadium shows in Norway at the end of this month. BBC Worldwide confirmed tickets are still on sale.
Other shows are due to take place in Sydney, Australia, in April, as well as several dates in the UK.
Top Gear's executive producer, Andy Wilman, described last year as an "annus horribilis" after accusations of racism and an incident in which the show's crew were forced to flee Argentina after it emerged they were using a Porsche with a registration plate which some suggested could refer to the Falklands conflict of 1982.