More than 21,000 people complained to the BBC after Jeremy Clarkson joked public sector strikers should be "shot in front of their families".
Following an uproar over his remarks on the The One Show, the Top Gear presenter said he did not mean to cause offence.
"I didn’t for a moment intend these remarks to be taken seriously – as I believe is clear if they’re seen in context," he said."If the BBC and I have caused any offence, I’m quite happy to apologise for it alongside them."
A BBC spokesman said: "The One Show apologised at the end of the show to viewers who may have been offended by Jeremy Clarkson's comments."
Clarkson made the comments on Wednesday evening following a day of widespread industrial action by public sector workers. "I'd have them all shot." he said when asked what he thought about the strikes. "I'd take them outside and execute them in front of their families."
BBC Breakfast said it had received 21,000 complaints and the trade union Unision threatened to take legal action against the TV presenter.
His comments came after expressing support for the strike, saying "this is the BBC" then balancing his praise with the execution comment.
Clarkson, famed for making controversial comments, has since flown out of the country to visit China.
According to the Times the BBC brought the controversy on itself, as Clarkson claims he told the shows producers of the details of the joke and was given the go-ahead.
This article has been updated to reflect a change in the number of complaints as reported by the BBC. It initially stated that there had been 23,000 complaints.