The new citizenship process could spark a series of by-elections and have consequences for the Government, Prime Minister Malcolm Turnbull has conceded.

Key points: Malcolm Turnbull says the citizenship debacle holds more potential risks for the Government

Malcolm Turnbull says the citizenship debacle holds more potential risks for the Government He urged any members remaining who believed they could be dual citizens to come clean and resign

He urged any members remaining who believed they could be dual citizens to come clean and resign The PM will talk to Bill Shorten tomorrow about the new citizenship measures

After months of revelations about parliamentarians being found to be dual citizens, Mr Turnbull has announced a plan to force MPs to release information about themselves and their parents.

But Liberal backbencher John Alexander may also be a dual citizen by descent because his father was born in the UK.

Mr Alexander said his father had become an Australian citizen as soon as he could.

"I understand he renounced his British citizenship before I was born because he was a proud Australian," he said in a statement.

The MP's status could be clarified if he can find evidence that his father renounced his British citizenship before Mr Alexander was born in 1951.

Mr Turnbull will hold talks with Opposition Leader Bill Shorten tomorrow about the new system for checking citizenship, but said it could mean more elections.

"If after all this information is out there, if the Parliament concludes that so many members and so many senators are either not solely Australian citizens or there is sufficient doubt about it, then they can be referred to the High Court," he told Radio National this morning.

More by-elections could be on the way

The recent High Court finding that former deputy prime minister Barnaby Joyce was a dual citizen has already caused a by-election, which leaves the Government temporarily without a clear majority.

"If the High Court concluded that there are a number of members of the House of Representatives that were not eligible to sit in the Parliament, then there would be a series of by-elections," Mr Turnbull said.

"Depending on the result of the by-elections, that could have consequences for the Government; I mean. that is obvious."

While conceding the citizenship issue holds more potential risks for his Government, Mr Turnbull would not say if Mr Alexander's case should be referred to the High Court.

"I am not going to start frontrunning this process," he said.

"We have got to respect the process that is set up in the electoral act and the constitution, people should make their declarations and then cases can be referred," Mr Turnbull said.

Last week, former Senate president Stephen Parry announced he was a dual citizen by descent and resigned.

Mr Turnbull said others should do the same if they knew they had dual citizenship.

"Obviously if a member believes that they are a dual citizen now and are ineligible to sit in the Parliament, then they should resign," he said.

"I take it as a given that every member of the House and the Senate as of today believes that they are eligible to sit in the House or the Senate."