The Morrison government’s threat to refer crossbench MP Kerryn Phelps to the High Court if the Parliament moves on Peter Dutton has sparked fresh claims of intimidation.

The New Daily reported Tuesday night that manager of government business Chris Pyne communicated the tit-for-tat warning to crossbench MPs in a move designed to shut down any push for the High Court to examine the Home Affairs Minister’s eligibility to sit in Parliament.

Mr Pyne confirmed the threat Wednesday morning on ABC radio, saying he would the take steps if Parliament referred Mr Dutton, but said a High Court examination did not represent a “threat”.

“We have very firm legal advice that Peter Dutton doesn’t have a Constitutional issue under Section 44,” he said.

“But if he does. If the Parliament decides that he does go to High Court, well that’s the same problem then that Mike Freelander and Kerryn Phelps has, and Tony Zappia has,” he said.

“It would behove the Parliament, if they sent Peter Dutton to the High Court, that those three MPs would also have to be referred to the High Court.

“If they decide that he does, if he wants to send them there, then they need to send those three as well.”

Independent MP Dr Phelps said that Mr Pyne had conveyed the warning directly to her colleague SA independent Rebekah Sharkie on Tuesday night at Parliament House.

“Well, I won’t be intimidated. And I think the Australian people will see right through it as a dirty tactic and a toxic culture that saw Julia Banks leaving the Liberal Party,” she told The New Daily.

Questions over Mr Dutton’s eligibility have swirled for months over whether government payments to his family’s childcare centre could represent an office for profit under the Crown for the purposes of section 44 of the Constitution.

Ms Sharkie said Wednesday the constitutional questions around Mr Dutton’s eligibility needed to be investigated.

“I think it’s quite clear that Peter Dutton has a case to answer … I think the best thing Peter Dutton could do would be to refer himself,” she said.

“I don’t think the government wants to be seen to be running a protection racket for Peter Dutton, which is what they’re sort of alluding to as far as I’m concerned.

“It’s a transparent attempt at intimidation over the Peter Dutton referral.”

Labor frontbencher Chris Bowen sad Mr Pyne’s threat of referrals was “pathetic”.

“What a pathetic attempt at smear by the dirt unit in the Liberal Party to try to link Dr Phelps,” Mr Bowen said.

“They can make threats about Dr Phelps or anybody they like, Mr Dutton is the one is constitutional questions to answer. Not anybody else,” he said.