Australia's rival political leaders have attacked each other 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.

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

Shorten complained Thursday that 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.

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