Australia's rival political leaders attacked each other on Thursday over the Parliament's citizenship crisis that is threatening to ensnare a growing number of lawmakers.

Prime Minister Malcolm Turnbull wants opposition leader Bill Shorten to support his plan to make all lawmakers provide proof that they have not breached a constitutional ban on dual citizens sitting in Parliament.

Any House of Representatives lawmakers who are disqualified as a consequence of an undisclosed second nationality would be replaced at by-elections early next year, which could potentially change the government.

But a day after a two-hour discussion on finding a bipartisan way forward, the two leaders remained divided.

Mr Shorten complained on Thursday that Mr Turnbull's citizenship test was inadequate and allowed lawmakers too much time to provide proof that they had not inherited another nationality from a parent or had renounced any other nationality.

Mr Shorten said the lawmakers should be given only five days to provide documented evidence that they were solely Australian, not three weeks as Mr Turnbull proposed.

"I don't think the nation can continue into the new year with this government crisis," Mr Shorten told Seven Network television.

Mr Turnbull accused Shorten of exploiting the crisis for political gain rather than cooperating on finding a solution.

"He has got to decide whether he wants to be part of the solution or continue to be part of the problem," Mr Turnbull told Nine Network television.

The citizenship test needs to be endorsed by Parliament and the conservative government needs the opposition centre-left Labour Party's support to get that endorsement from the Senate.

Australia is rare if not unique in the world in banning dual nationals from sitting in Parliament.

The constitutional quirk had rarely been an issue in its 116-year history, although many dual citizens are suspected to have escaped detection.

Only two elected lawmakers had ever been disqualified over foreign citizenship, in 1996 and 1998, before the current Parliament was elected in 2016.

Investigations by political enemies and journalists resulted in the High Court last month disqualifying five lawmakers in a strict interpretation of the ban.

The court rejected the government's argument that ignorance of an inherited nationality should be accepted as an excuse.

A sixth senator resigned last week after revealing he had inherited the citizenship of his British-born father.

Most crucial is the fate of lawmakers in the House of Representatives where parties need a majority of seats to govern.

Senators are replaced usually from members of the same party without elections.

So far, only Deputy Prime Minister Barnaby Joyce has been disqualified from the lower house, reducing the government's majority in the 150-seat chamber from 76 seats to 75.

John Alexander, a lawmaker in Mr Turnbull's Liberal Party, announced this week that he was waiting for advice from the British Home Office on whether he had inherited citizenship from his English-born father.

Several Labour lawmakers in the House of Representatives are also under a cloud, including Justine Keay.

The British government officially renounced her citizenship on July 11 last year - nine days after she was elected. The High Court has said what counts was her status when she nominated for election - June 9.

Many argue that the dual citizen ban is increasingly inappropriate for a migrant nation where half the population is an immigrant or has an immigrant parent.

But changing the constitution requires all registered voters to cast ballots at referendums, which rarely succeed.

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