Greens senator Sarah Hanson-Young is seeking legal advice about what she says are “offensive and sexist slurs” from Senator David Leyonhjelm – and has called on him to quit Parliament.

The Greens will also try to have Senator Leyonhjelm censured by Parliament, following his remarks on Sunday’s Outsiders program on Sky News, alluding to rumours about Senator Hanson-Young’s private life.

On Sunday, Sky News apologised for broadcasting and strap-lining what it described as Senator Leyonhjelm’s “appalling” remarks. It also suspended a producer.

Senator Leyonhjelm was invited onto Sunday’s program because last week he had shouted “stop shagging men, Sarah” while Senator Hanson-Young was debating a motion in the Senate to allow women to carry weapons for self-defence.

Yesterday, Senator Hanson Young confirmed on Twitter that she was seeking legal advice about the comments.

“Thank you for all the words of support and case; they mean a lot to me,” she wrote.

Thank you for all the words of support and care; they mean a lot to me. I am seeking legal advice – as many of you have suggested. As a woman, a sister and a mother, I will continue to stand up. I will not be intimidated or bullied by offensive & sexist slurs.

— 💚🌏 Sarah Hanson-Young (@sarahinthesen8) July 2, 2018

Later, she said Senator Leyonhjelm should do the decent thing and resign.

“I believe he has proven himself incapable of showing respect and is unfit to represent not only women, but all decent Australians, in our nation’s parliament,” she said.

On Monday, deputy Liberal leader Julie Bishop and cabinet minister Simon Birminghan called on Senator Leyonhjelm to publicly apologise.

“The comments were highly disrespectful and we need more respect in public life, not less,” Ms Bishop said in Melbourne.

Senator Birmingham said there was no place for such commentary in decent and fair public policy.

“I would expect that apologies would be the appropriate order of the day. Frankly, people ought to be a little bigger and better than that,” he told Sky. “It’s certainly not the way I conduct my politics.”

Former prime minister Tony Abbott also joined the calls for the Liberal Democrats senator to say sorry for doubling down on his original attack.

“Leyonhjelm goes on Sky on the weekend in a very smug and self-righteous way and repeats the damn thing. People should be better than that,” Mr Abbott told Sydney radio.

Greens leader Richard Di Natale has called on Prime Minister Malcolm Turnbull and Opposition Leader Bill Shorten to also condemn the comments.

Meanwhile, Senator Leyonhjelm said there was no way he would apologise. Asked about the prospect of legal action and parliamentary censure, he responded with the ancient Greek expression of defiance “molon labe”, which roughly translates as “come and take”.

Viewers and commentators were also upset about the Outsiders content. Sky News presenter David Speers said the comments were sexist and “should have been called out” by the program’s hosts – former Liberal MP Ross Cameron and The Spectator editor Rowan Dean.

-with agencies