Waiting game for US-bound refugees

The waiting game continues for refugees on Nauru and Manus Island hoping for a swift resettlement in the US.

Malcolm Turnbull has confirmed US President Donald Trump will honour a deal the government struck with the previous Obama administration.

But the deal still lacks a timetable.

"I thank President Trump for his commitment to honour that existing agreement," the prime minister told reporters in Canberra on Monday.

There was some initial doubt whether Mr Trump would honour the agreement, given the president's ban on taking in people from seven countries which he said were "sources of terror".

Mr Turnbull declined to provide further details on the resettlement agreement, saying screening was now in the hands of US officials.

Immigration Minister Peter Dutton flagged the process could take some time because of the rigorous checks involved.

He delivered a strong message to people smugglers looking to capitalise on the US deal to attract more asylum seeker boat customers.

"The resolve of this government has not diminished at all," he told reporters, adding air and boat patrols had been stepped up.

Deputy opposition leader Tanya Plibersek said the government needed to remove the "shroud of secrecy" surrounding the deal.

"It has taken way too long for people on Manus Island and Nauru to be resettled," she told reporters in Sydney.

Greens senator Nick McKim cast doubt over President Trump's assurances.

""Only a fool would trust Donald Trump when he says anything at all - he's a pathological liar," he told reporters in Hobart.