Australia has been given assurances its dual nationals will be exempt from a US immigration ban.

Prime Minister Malcolm Turnbull confirmed the development following a call from Australia's ambassador to the US in Washington, Joe Hockey.

"Australian passport holders will be able to travel to the United States in the same way they were able to prior to the executive order," Mr Turnbull told Sky News on Tuesday.

Mr Turnbull has come under fire for not joining other world leaders in publicly condemning President Donald Trump's executive order imposing a temporary ban on people from seven majority-Muslim countries.

Prime Minister Turnbull confirmed the news after his first official phone call with President Trump. More

"When I need to ... give frank advice, fearless advice to the United States government, I do so privately," he said.

"To do my job, which is to advance Australia's interests, protect Australian citizens, ensure that Australians can travel to and from the United States in the normal way, to do that, it is best that I reserve my comments on American domestic policy for private discussions with the president or his senior officials."