Australian Foreign Minister Julie Bishop has refused to express confidence a refugee swap with the United States will go ahead, after the chief diplomat had her first high-level interaction with President Donald Trump's administration.

The deal, struck in November under President Barack Obama, was to see 1800 refugees held in Australian offshore detention centres resettled in the US, but President Trump has thrown the agreement into doubt.

A leaked draft executive order from the White House reported by US newspapers on Thursday includes a four-month suspension on accepting refugees and a range of long-term restrictions. Speaking after a dialogue on Australia-US relations in Los Angeles on Thursday, Ms Bishop said she took a phone call that afternoon from US Vice President Mike Pence and had a "warm and engaging discussion" about a "whole range of issues".

Ms Bishop would not say if the refugee swap had been discussed with anyone in the new administration, or if she had confidence it would go ahead. "I believe the United States and Australia will continue to work together to assist each other in implementing our strong border protection policies," she said.