The KAP doesn't take a position on the issue, believing it's a matter of conscience for individual party members.
But Mr Gaynor issued a statement saying Mr Katter had "a moral obligation to protect life".
"It is the right thing to do," it said.
"Bob Katter will be asked, one way or the other now, about his position on abortion."
But when Mr Katter was asked by AAP for his own position, he became irate.
"We are sick and tired of you people trying to paint us as some sort of extremist organisation," he yelled down the phone.
"You're just trying to do to us what you did to Pauline Hanson.
"We spend none of our time talking about any of these things, and that's all you ever talk about.
"No wonder this country is the way that it is when we've got a journalistic cadre that can't think beyond this sort of extraordinary business."