Bill Shorten will urge Malcolm Turnbull to fast-track a new process to check MPs’ citizenship when the two leaders meet in Melbourne on Wednesday.

The Prime Minister needs Labor’s support for a plan to force all members and senators to declare on the register of interests that they are not a citizen of another country and set out the birth records of themselves and their parents.

If they have previously held citizenship of another country they must provide evidence of their renunciation or how it came to an end.

Under Mr Turnbull’s plan, the register would not be published until after Christmas.

Mr Shorten will argue it needs to be done sooner in order to provide the public with confidence that all MPs are eligible to sit.

As well, Labor is concerned the government is taking a go-slow approach to Liberal MP John Alexander.

However, it has emerged two Labor MPs, Tasmania’s Justine Keay and Queensland’s Susan Lamb, may be caught up in the citizenship debacle.

Ms Keay says her renunciation of British citizenship was not effective until after the 2016 election, while Ms Lamb has said she took all necessary steps to renounce her British citizenship in May 2016, but has not said if this was confirmed before the deadline, the Guardian online reports.

The recent High Court ruling stated Section 44 “does not disqualify only those who have not made reasonable efforts to conform to its requirements”.

Mr Alexander is seeking advice from UK authorities on whether he holds citizenship by descent through his British-born father – a case virtually identical to that of disqualified senator Fiona Nash and resigned senator Stephen Parry.

He believes he is solely an Australian citizen, but has promised to make a full statement once the advice is received.

Labor says the MP for Bennelong should be referred to the High Court.

However, the Prime Minister says all MPs should be allowed to make their declarations under the new process and then cases can be referred to the court.

If Mr Alexander is disqualified from parliament, the government – which holds a one-seat majority and is already fighting a by-election in New England – would be forced to a by-election in Bennelong, which the MP holds with a 7.8 per cent margin.

Liberal senator Eric Abetz said he hoped there would only be a “limited number of by-elections”, but a general election could not be ruled out.

Former Liberal senator turned independent Cory Bernardi suggested the best solution would be to prorogue the parliament.

Liberal MP Rowan Ramsey admitted the problem had become a “frustration” but was hopeful the government can put the “sideshow” behind it.

“The people in the pub and down the golf club, they just think the whole world’s gone mad and why can’t Canberra get it right,” he told ABC radio.

– AAP