Greens senator Sarah Hanson-Young is demanding David Leyonhjelm pay her compensation for "hurt, distress and embarrassment" over his comments toward her.
Senator Leyonhjelm said he has received a "concerns notice" from a legal firm acting for Senator Hanson-Young, but would not be apologising.
The lawyers' notice demands an apology and "compensation of a monetary amount determined by Senator Hanson-Young" within seven days.
The notice claims the Liberal Democrats senator caused her "hurt, distress and embarrassment" over comments he made in the media between July 1 and July 4 regarding her opinions about men.
"Senator Hanson-Young's action is without merit," Senator Leyonhjelm said in a statement on Thursday.
"She is also wasting her time, money and endless reserves of outrage, because I will not be issuing an apology."
Senator Leyonhjelm believed he heard Senator Hanson-Young say in parliament last week words to the effect of "all men are rapists" - which she denies - and responded with "stop shagging men".
He has alluded to her private life in subsequent media interviews.
He said apologising in response to the outrage of a "politically correct lynch mob" would be insincere.
"Senator Hanson-Young has a history of saying derogatory and sexist things about men and implying that all men are collectively responsible for the crimes of a few," he said.
He said many men were fed up with being collectively blamed for the "actions of a few sick individuals who assault, rape and murder".
