The public feud between Malcolm Turnbull and Kevin Rudd has escalated, with the former Labor leader accusing the Prime Minister of lying about their private discussions on asylum seeker policy.

Mr Rudd has challenged Mr Turnbull to provide evidence to support his repeated assertions that he "begged" Mr Rudd not to dismantle the Pacific Solution policy introduced by John Howard to stop the boats.

He has branded the Turnbull account a "total reinvention of history" to "try and pretend he has had a consistent position on Manus and Nauru", saying Mr Turnbull was not even opposition leader when the policy was dismantled.

The charge came as Mr Turnbull branded Mr Rudd a "liar" in an address to his MPs and used the Parliament to ramp up pressure on Labor to support the Coalition's lifetime ban on refugees processed offshore visiting Australia, with Immigration Minister Peter Dutton suggesting the move was a precursor to refugees being resettled from Nauru and Manus Island.