Public sector union Unison is considering taking legal action against Jeremy Clarkson after he said people who went out on strike "should be shot".
The BBC was forced to apologise after the Top Gear presenter joked that it was unfair for people in the public sector with "gilt edge pensions" to stage a walkout "when the rest of us have to work for a living".
"I'd have them all shot." he said. "I'd take them outside and execute them in front of their families."
Dave Prentis, Unison's general secretary, said: “Clarkson’s comments on the One Show were totally outrageous, and they cannot be tolerated.
"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."
"An apology is not enough - we are calling on the BBC to sack Jeremy Clarkson immediately. Such disgusting statements have no place on our TV screens."
David Cameron said Clarkson's comments were "silly" but he fell short of condemning the presenter who is a friend of his.
Speaking on ITV's 'This Morning' programme on Thursday, the prime minster said: "It's obviously a silly thing to say. I'm sure he did not mean that."
Clarkson is part of the so-called 'Chipping Norton set' of friends centered around Cameron's Oxfordshire constituency that also included former News of the World editor Rebekah Brooks.
Karen Jennings, Unison assistant general secretary, told Sky News that Clarkson's comments were "almost inciting anger and hate towards public sector workers" and called for Cameron to go further in his condemnation.
"The prime minister has a record on this, he does seem to stand by his friends in the face of criticisms of what they do or what they say," she said.
Jon Trickett MP, Labour's shadow minister for the Cabinet Office, had called for the prime minister to "disassociate" himself from the remarks made by Clarkson.
"No one wants these strikes but most of today's strikers are mums, not militants. Clarkson should apologise. And the prime minister should make clear he disassociates himself from the distasteful remarks uttered by one of his friends," he said on Wednesday night.