Malcolm Turnbull is adamant he will use his parliamentary numbers to unilaterally refer Labor MPs under a dual citizenship cloud to the High Court, saying the issue is an "acid test" for Bill Shorten's integrity.

The prime minister insists the move is a matter of conscience, not political tit-for-tat, despite Labor saying it has robust checks on its MPs' eligibility.

Nine federal MPs have resigned or been found ineligible by the High Court to sit in parliament because they held dual citizenships, which is barred by section 44 of the constitution. None are from Labor.

Senators' family history and citizenship details will be published on Monday, with the same disclosures for lower house members due on Tuesday night and set to be made public on Wednesday.

Based on what he has seen from coalition MPs' paperwork, Mr Turnbull says he is satisfied there will not be any further problems, but he does not think the opposition can be as confident.

"There are plainly a number on the Labor side which should be referred to the High Court," he told Sky News on Sunday.

The matter is an "acid test" of the opposition leader's integrity.

"We can't in good conscience fail to refer anyone - whether on our side or on Labor's side or on the cross bench - to the High Court if it is clear there are substantial grounds for believing that they are ineligible to sit in the parliament," Mr Turnbull said.

"I say this without any partisanship at all. I would say the same thing about one of our members."

The High Court made a literal interpretation of the law, ruling that candidates for parliament had to be only Australian citizens at the time of their nomination.

Based on previous rulings, it had been thought it was enough to have taken reasonable steps to renounce any other allegiances.

A number of Labor MPs and NXT's Rebekha Sharkie filed paperwork to renounce British dual citizenship ahead of the 2016 election but did not receive confirmation from the UK before nominating.

Opposition frontbencher Tim Hammond says Labor still has faith in its vetting processes.

"Those MPs that the Liberal party like to try and shine a spotlight on have all taken very conscious and deliberate steps to renounce," he told Sky News.

"What we see in relation to the Liberal party and the National party here is, quite frankly, just blind ignorance in relation to a position that could have well been sorted out and revealed many years ago."

Meanwhile, former senators Jacqui Lambie, Stephen Parry and Skye Kakoschke-Moore face a High Court hearing on December 8 after discovering they held dual citizenship.