In his first talks with Prime Minister Malcolm Turnbull since taking office, US President Donald Trump has confirmed he will honour the deal to resettle Nauru and Manus Island asylum seekers.

The confirmation came after a 25-minute phone call between the leaders, emphasising the “enduring strength and closeness” of the US-Australia relationship, the White House said in a statement.

Trump and Turnbull spoke at around 9.00am on Sunday. Photo: AAP

The refugee resettlement deal’s future, which was made last year with the Obama administration, came into question just days ago when Mr Trump signed an executive order suspending his country’s refugee program.

Mr Trump’s hardline stance on refugees was loosened, however, as he vowed to honour the deal to resettle refugees from Nauru and Manus Island in the US, according to reports.

“Both leaders emphasised the enduring strength and closeness of the US-Australia relationship that is critical for peace, stability and prosperity in the Asia-Pacific region and globally,” the White House said.

Neither the White House’s statement nor Mr Turnbull’s office made mention of the issue and have not released any further details.

It’s unclear how many of the around 2000 asylum seekers held on Nauru and Manus will be resettled in the US.

US officials visited Nauru under the Obama administration to conduct first-round interviews and were due to begin screening applicants on Manus Island in mid-February.

Mr Turnbull hoped the resettlement deal could be spared from Mr Trump’s suspension of refugees, with an executive order stating officials can still admit refugees under pre-existing international agreements.

“We are very confident and satisfied that existing arrangements will continue,” Mr Turnbull said before the call.

“It’s quite clear that the administration has set out in the order the ability to deal with existing arrangements.”

The executive order released by Mr Trump over the weekend also included a four-month pause on all refugee arrivals in the US, a three-month ban on entry by citizens from seven countries of terrorism concern including Iran, Iraq and Syria, and an indefinite halt on all refugees from Syria.

Mr Turnbull and Mr Trump also discussed the war against terrorism, trade, global security in the Asia-Pacific region, and their shared interest in stopping irregular migration of people seeking asylum.

The President also spoke with Japanese Prime Minister Shinzo Abe, German Chancellor Angela Merkel, Russian President Vladimir Putin, and French President Francois Hollande on Sunday.

PM pleased with Trump chat: Julie Bishop

Minister for Foreign Affairs Julie Bishop refused to confirm the refugee deal was discussed. Photo: AAP

Foreign Affairs Minister Julie Bishop said Mr Turnbull was “pleased with the outcome” of his discussion with Mr Trump, although she declined to say if the asylum seeker deal was raised.

Ms Bishop, who was in Los Angeles on Saturday (US time) to attend the G’day USA trade and cultural gala, confirmed she has had a second conversation with US Vice-President Mike Pence.

“I’ve had two very constructive conversations with Vice-President Pence and I know the Prime Minister was pleased with the outcome of the discussion he had with the President today,” she said, adding Mr Turnbull would travel to the US for a yet-to-be-scheduled meeting with Mr Trump.

Ms Bishop first spoke with Mr Pence last Thursday when she congratulated him on the presidential inauguration.

White House staff confirmed the Vice-President thanked Australia for its “steadfast partnership and contributions around the globe”.

“The two reaffirmed the importance of continuing to strengthen the US-Australia alliance to maintain peace and security in the region,” the statement read.