Michael Fabricant made the comments about high profile left wing journalist Yasmin Alibhai-Brown after she clashed with right-wing commentator Rod Liddle on a television news programme.
He wrote on Twitter: “I could never appear on a discussion prog with @y_alibhai I would either end up with a brain haemorrhage or by punching her in the throat.”
The “disgusting” comments sparked a furious backlash and immediate calls for him to issue a full apology, including from Tory high command.
A Conservative spokesman said: “Mr Fabricant’s comments were completely unacceptable, in poor taste and he should immediately apologise.”
Labour’s Gloria De Piero, shadow minister for women and equalities, said: “Michael Fabricant’s tweet is utterly appalling and he must apologise personally to Yasmin Alibhai-Brown immediately.
“It is unacceptable that views like this persist in the Conservative Party. David Cameron needs to be clear about this and set out what action he will be taking.”
Over a series of tweets, Mr Fabricant attempted to make amends for the comments, telling Ms Alibhai-Brown she was “utterly infuriating” but he would not have actually punched her.
He wrote: “Just out of dentist. 1 It appears that some people who don’t know me think I actually go round punching ‘in the throat’. Not true.
“2. If anyone believes I would seriously threaten someone with violence, I of course withdraw and apologise.
“3. I am afraid I know I would get v angry if I had been on the Ch4 debate last night. Glad it was Rod Liddle and not me!
“Sorry @y_alibhai if you actually thought I would punch you. I actually don’t do that sort of thing. But you are utterly infuriating! xx”.