From Vietnam, where he is attending the APEC summit, the prime minister has threatened to use the government’s slim majority in the lower house to refer to the High Court any MP whose eligibility to sit in parliament is in doubt because of their dual citizenship status.

That’s brought an angry response from Labor, which faces the prospect of four of its MPs – Justine Keay, Madeleine King, Susan Lamb and Josh Wilson – being disqualified from parliament.

Opposition Senate leader Penny Wong accused Turnbull of behaving like a “tin-pot dictator”.

“This is really a very desperate and diminished prime minister we’ve seen,” she told FIVEaa radio in Adelaide today.

“I think Australians, who are rightly sick of this, want it resolved.”

Frontbench colleague Anthony Albanese told the Nine Network the government was “melting down before our eyes” while cabinet minister Christopher Pyne accused Opposition Leader Bill Shorten of trying to “blow up the parliament”.

Greens leader Richard Di Natalie told Sky News a “slightly unhinged” prime minister was losing the plot.

The minor party was considering petitioning the governor-general to dissolve parliament and call a general election, he said.

Turnbull has told South Australian independent MP Rebekha Sharkie she may have to refer herself to the High Court over the timing of her renunciation of British citizenship before the 2016 election.

The Nick Xenophon Team MP lodged her paperwork on April 19 and received confirmation of receipt on June 2.

Sharkie nominated for the seat of Mayo on June 7, two days before nominations closed.

But it was on June 29 the Home Office registered her renunciation.

“I believe that I took all steps that were required by the UK to renounce any entitlement to UK citizenship, that were within my power to do so,” she said.

“I had no control as to the speed at which the UK Home Office processed my application.”

On the government side, there are reports Liberal backbencher John Alexander could quit his Sydney seat as early as this weekend because he believes he is a British citizen by descent.

Turnbull is in Asia until next Wednesday after being unable to broker a deal with Shorten over a citizenship disclosure scheme.

The Labor leader argued for a December 1 deadline for MPs to declare their status and provide High Court standard details of their family history and any renunciation steps.

He also called on Turnbull to follow the established precedent of no partisan referrals.

The prime minister dismissed Shorten’s request as “unworthy”, saying the Coalition had earlier referred its MPs to the High Court despite advice they were in the clear.

There were now Labor MPs who freely admitted they were UK citizens at the time they nominated for parliament, Turnbull said.

“It really is a bit rich of Mr Shorten to say to me that the government shouldn’t vote to refer them,” told reporters in Da Nang.

Turnbull has proposed December 7 – the final scheduled sitting day of parliament for the year – as the deadline for MPs to lodge their documents.

But it would rule out any High Court referrals until the parliament next sat, either on a sitting day added to the 2017 calendar or February 5 when it’s scheduled to resume in 2018.

The Senate comes back for a week of sitting on Monday, but the government lacks the numbers on its own to force a disclosure scheme on the upper house.

– with AAP