The centre-right government of Australian Prime Minister Malcolm Turnbull has been thrown into turmoil after the revelations that his deputy has been entangled in an extra-marital affair, straining the alliance between his Liberal Party and the National Party of Barnaby Joyce.

Joyce will take a break next week rather than step in for the country's leader while the PM is away, as a poll shows his popularity plummeting since admitting to a sex affair with a former staffer.

Joyce, a Catholic who campaigned on "family values" and been married for 24 years, is expecting a child with his former press secretary.

Joyce has so far resisted calls to quit either his seat or his cabinet spot, including a motion that passed the Senate calling for his resignation, since leaving parliament would put the government's narrow one-seat majority at risk.

"The deputy prime minister will be taking leave from Monday ... and accordingly will not be able to be acting prime minister while I'm overseas," Turnbull said above loud heckling in parliament.

Joyce's break, while Turnbull travels to Washington to meet US President Donald Trump, comes after an opinion poll showed support for the plain-spoken small-town accountant turned politician had tumbled in his rural electorate.

The percentage of voters backing him crashed to 43 percent, according to the ReachTEL poll published in Fairfax newspapers on Thursday, down from the 63 percent margin he won at a by-election in December.

His week off also comes as pressure intensifies over his failure to declare the relationship with his former press secretary, Vikki Campion, when she was hired for two highly paid government positions outside his office.

Australia's ministerial code of conduct requires legislators to declare relationships with any staff member of a cabinet minister.

There are also questions about Joyce's acceptance, rent-free, of a townhouse belonging to a wealthy friend, Greg Maguire, and whether Joyce broke ministerial rules forbidding asking for gifts. Joyce denied asking for the townhouse.

"Most people would realise that at the time of a marriage break-up, it is not unusual for those who you are close to, to offer support," he told parliament.

"Mr Maguire approached me ... he said: 'You're living out of a suitcase, and this is basically something that I should try and help you with.' I took him up on the offer but I offered to pay for it."

He has also said he did not break any rules over Campion's employment because she was not his "partner" at the time.