Donald Trump may be drawing attacks for his tough stance on immigration, but he is understood to have assured Malcolm Turnbull the refugee arrangement between the two countries will stand under his presidency.

The prime minister held a 25-minute phone call with Trump today, their first conversation since the billionaire's inauguration as US president last weekend.

It came just days after Trump's decision to put a four-month block on refugees entering the US.

Turnbull struck a "one-off" deal with former US president Barack Obama in November to resettle refugees detained on Manus and Nauru in the US.

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Trump confirmed his administration would continue to honour the 2016 refugee resettlement arrangement while acknowledging a common interest in preventing irregular and illegal migration.

The two committed to making the long-standing relationship between the two countries even stronger and sharing the ongoing objective to defeat Islamic State.

They will continue to work together to improve global instability, including in the Asia-Pacific.

"Both leaders emphasized 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 in a statement.

Foreign Affairs Minister Julie Bishop said Turnbull was "pleased with the outcome" of his discussion.

Speaking to reporters at the G'day USA gala in Hollywood, Bishop said Turnbull would travel to the US for a yet to be scheduled meeting with the president.

Trump has come under fire after signing an executive order putting a temporary stop to refugees and people from certain countries entering the US, but he said that the step was "not a Muslim ban".

Deputy Labor leader Tanya Plibersek said every country had the right to do strong background checks on people that they were considering for permanent residency or citizenship.

"But those background checks shouldn't be based on assumptions based on a person's country of origin, ethnicity or religion," she told reporters in Sydney.

"For 40 years Australia has had a non-discriminatory immigration policy, and our Australian government needs to be crystal clear that that will continue in Australia."

Greens Leader Richard Di Natale said Turnbull must take a stand against Trump's immigration decision.

"We have got to make a choice, we are either a lap dog to the US and fall in behind them no matter what they do ... or we take a stand and we recognise there has to be a line drawn around what are moral issues," Senator Di Natale told Sky News.

The call to Turnbull, in the presence of the president's chief strategist Stephen Bannon and national security adviser Mike Flynn, was the last of a series of calls from the Oval Office to world leaders.

German Chancellor Angela Merkel and Trump are reported to have agreed on the fundamental importance of the NATO alliance and that all NATO members must pay a fair share for their collective security.

Russian President Vladimir Putin and the US president also want to co-operate in Syria to defeat Islamic State.

But French President Francois Hollande warned Trump against taking a protectionist approach, saying it would have economic and political consequences.