Jeremy Clarkson should be sacked by the BBC over his "appalling" comments about killing striking public sector workers, trade union Unison has said.
The union said it was considering reporting the Top Gear presenter to the police over comments on The One Show.
Referring to striking workers, Mr Clarkson said: "I'd have them all shot. I would take them outside and execute them in front of their families."
The BBC received over 4,700 complaints and has apologised for the comments.
Mr Clarkson's comments, on Wednesday's screening of the BBC One show, sparked hundreds of responses to be posted on social networking site Twitter.
Talking about the strikes over pension changes, Mr Clarkson also said: "I mean, how dare they go on strike when they've got these gilt-edged pensions that are going to be guaranteed while the rest of us have to work for a living?"
Some of his remarks, which appeared to have been made in a lighthearted tone, were greeted with laughter from a studio audience, as did his comment that the strikes were "like being back in the 70s" which made him feel "at home, somehow".
Dave Prentis, general secretary of Unison, said: "Clarkson's comments on The One Show were totally outrageous, and they cannot be tolerated.
'Silly thing to say'
"An apology is not enough - we are calling on the BBC to sack Jeremy Clarkson immediately.
"We are seeking urgent legal advice about what further action we can take against him and the BBC, and whether or not his comments should be referred to the police."
He added: "Jeremy Clarkson clearly needs a reminder of just who he is talking about when he calls for public sector workers to be shot in front of their families.
"Whilst he is driving round in fast cars for a living, public sector workers are busy holding our society together - they save others' lives on a daily basis, they care for the sick, the vulnerable, the elderly."
Prime Minister David Cameron, asked about Mr Clarkson's comments during an appearance on ITV's This Morning, said it was "a silly thing to say... I'm sure he didn't mean it".
Labour leader Ed Miliband said: "Jeremy Clarkson should apologise for those comments. He obviously does not understand the lives of the people who were going out on strike yesterday."
Pensions Minister Steve Webb also said it was "a stupid thing to say".
"He should apologise and we should get on with our lives," said the minister.
Tens of thousands of people joined rallies around the UK on Wednesday as a public sector strike over pensions disrupted schools, hospitals and other services.
About two-thirds of state schools shut, and thousands of hospital operations were postponed, as unions estimated up to two million people went on strike. The government disputes this figure.
Unions oppose plans to make members pay more and work longer to earn what they say will be smaller pensions.
During The One Show, Mr Clarkson also made a remark about people who threw themselves in front of trains.
Later One Show presenter Matt Baker made an apology during the show about those comments.
A BBC spokeswoman said that apology should also be taken to apply to his joke about shooting strikers.