Senator Reynolds has taken extended sick leave after facing intense scrutiny over her handling of rape allegations raised by former staffer Brittany Higgins.

The prime minister denies her position has become untenable.

“Linda Reynolds on a cardiologist’s advice has been asked to take that month off,” he told Seven on Thursday.

“If that had happened to any other Australian, I’m sure they’d want simply that person to get well and to listen to their doctors and to get the treatment they need, and that’s what’s occurring.”

Morrison insisted the government “was not skipping a beat” in the defence portfolio.

“We’re just getting on with the job.”

Meanwhile, a key crossbench senator has warned Morrison the Christian Porter saga will become an “albatross around his government’s neck” unless action is taken.

Independent senator Rex Patrick holds a crucial vote on the government’s industrial laws which the government is hoping to get through the upper house as soon as possible.

Porter, the attorney-general and industrial relations minister, will miss parliament next week as he deals with mental health issues arising from an allegation of historical rape which he strongly denies.

Next Thursday is the last Senate sitting until the May budget.

Morrison has resisted calls for an independent inquiry, saying NSW police have declared the case closed and Mr Porter is an “innocent man under our law”.

However, Patrick says Porter needs to lead talks with the crossbench on the proposed laws and it is “impossible” to make progress until he returns to work.

Patrick dismissed Morrison’s insistence there was nothing more he could do.

“That may suit him politically, but he is a little bit naive in that this will become an albatross around his government’s neck if he does not act to clear Christian Porter, not from a criminal offence but from the questions as to whether or not he is fit to hold high office.”

The South Australian senator suggested former public servant Dr Vivienne Thom be called in, having previously investigated the conduct of former High Court judge Dyson Heydon and the expenses scandal within the corporate watchdog ASIC.

“He has to have his name cleared so that he enjoys the trust of government and indeed the trust of the Australian public,” Senator Patrick told the ABC.

Labor frontbencher Jim Chalmers said it was another sign of a government in crisis.

Health Minister Greg Hunt is also on leave after developing an infection, depriving the government of three senior ministers.