Malcolm Turnbull is confident his government's new refugee deal with the United States will continue under a Trump administration.
However, the prime minister has declined to say how many refugees in detention on Manus Island and Nauru will be taken in by the US.
US president-elect Donald Trump strongly campaigned on banning Muslim migration and putting up a wall to keep Mexicans out.
Mr Turnbull said the deal was struck with the Obama administration and the issue had not been raised with Mr Trump.
"We deal with one administration at a time. You don't discuss confidential matters with one administration with a future administration," he said.
About 1600 people on Nauru and Manus Island would be eligible, but the numbers and assessment of people would be up to the United Nations High Commissioner for Refugees and the US government, he said.
The timing would also be up the US, however it would not apply to any future boat arrivals.
The prime minister acknowledged people smugglers could use it as a "marketing opportunity" but Operation Sovereign Borders' surveillance and response would be stepped up.
Asked whether he agreed that, if those people weren't processed and relocated before Mr Trump moves into the White House on January 20, that the deal is unlikely to happen, Mr Turnbull told ABC's 7.30: "You are entitled to speculate about that, but I'm confident that the arrangements that we've set in place will continue.
"We have a very long history of co-operation with the United States where we, in matters of this kind, are able to pursue our mutual and our respective humanitarian and national security objectives."
Labor leader Bill Shorten, whose advisers were briefed on the deal on Monday, said the opposition would take a "constructive approach".
"Where the case is made, where the evidence is put forward, where there is something positive, we will be up for making that work," he said.
The UNHCR wants the government to find a solution for all asylum seekers in offshore detention.
"It's important that they don't remain in Nauru and Papua New Guinea, where they've stayed for far too long and indeed languished in limbo," external relations officer Catherine Stubberfield told ABC radio.
A prominent US anti-immigration think tank has warned the deal won't last Mr Trump's first day as president.
"My sense is that when the word gets out on this, it'll be dead on arrival," Mark Krikorian, executive director of the influential Centre for Immigration Studies, told Fairfax Media.
"I don't expect any Republicans will defend it; I can't see a lot of Democrats defending it either."
Refugee Council president Phil Glendenning described the deal as a vital first step.
But One Nation Leader Pauline Hanson is not happy.
"I feel for the American people. They are going to get these refugees, that it is not their responsibility at all," she told the Seven Network.
Immigration Minister Peter Dutton is upping the pressure on Labor to back the government's plan for a lifetime visa ban on asylum seekers arriving by boat, as a precursor to the US deal.
Mr Shorten said he had been informed the Americans had not sought the lifetime ban as part of the deal.
"Let's not play politics with this issue. What matters here is stopping the people smugglers," he said.