"Mr Priebus and Mr Bannon had a productive meeting with the Australian ambassador at the White House," the White House official said on Thursday.
"They conveyed the president's deep admiration for the Australian people."
Mr Trump said on Thursday he loves Australia and will honour the deal struck by his predecessor but only refugees who pass extreme vetting will be allowed into the US.
"If a previous administration does something you have to respect that but you can also say 'Why are we doing this?'" Mr Trump, speaking to reporters before a meeting at the White House with US steelworkers, said.
Mr Trump questioned the refugee agreement in his blunt, exclamation-laden style on Twitter on Wednesday night when he described it as "a dumb deal!"
This was after .
Watch: Talking with Turnbull 'worst call by far', Trump says
The article, Mr Trump's reported treatment of Mr Turnbull and more inflammatory comments at a Washington DC prayer breakfast on Thursday morning about Australia and other allies had some analysts predicting the strong alliance could be damaged.
Later in the day Mr Trump eased his rhetoric about Australia.
"I have a lot of respect for Australia," he said at the steelworkers' meeting.
"I love Australia as a country but I have a problem where for whatever reason president Obama said they were going to take probably well over 1000 illegal immigrants who were in prisons."
Mr Trump said the initial potential number of refugees could be 1250 but questioned whether it "could be 2000, could be more than that and I said 'Why? Why are we doing this?'"
RELATED READING
Trump call to Turnbull was harmful: McCain
White House spokesman Sean Spicer confused the issue further on Thursday when he described the phone call between Mr Trump and Mr Turnbull as "cordial", although at a chest-beating speech earlier at the prayer breakfast Mr Trump did not describe it that way.
"When you hear about the tough phone calls I'm having, don't worry about it," he told the audience of political and religious leaders.
"We have to be tough.
"It's time we have to be a little tough folks.
"We are taken advantage of by every nation in the world virtually."
RELATED READING
Americans react on Twitter to the Turnbull-Trump phone call
Damage control
Senior Republicans have gone into damage control mode to ease fears about the Australian-US alliance.
"Australia is a very central ally," US House of Representatives Speaker Paul Ryan told reporters.
"They are and will continue to be."
Senator Lindsey Graham took aim at Mr Trump's use of Twitter, telling CNN he wished he "would sleep more and tweet less".
The former member of the US Air Force who worked alongside the Australian military in Iraq and Afghanistan and whose father was stationed in Australia during World War II, said the alliance would survive.
He also showed support for the asylum-seeker deal.
"The relationship is strong and can withstand a phone call," Senator Graham said.
"We'll be fine with Australia.
"The 1250 refugees we are talking about, if they are well vetted, we can absorb them."
Senator John McCain, a Vietnam war hero, phoned Australia's US Ambassador Joe Hockey to "express my unwavering support" for the US-Australian relationship and described Mr Trump's treatment of Mr Turnbull as "unnecessary and frankly harmful".
"Australia, they fought alongside us in wars including losing over 500 brave Australians in the Vietnam War, which some of us remember," Senator McCain told reporters on Capitol Hill.
Under the Obama-Turnbull refugee deal Australia would accept refugees from central America.
Former Australian Prime Minister Kevin Rudd believes the Australia-US relationship is old enough and ugly enough to overcome the Trump-Turnbull "snafu".
Mr Rudd is playing down the reportedly hostile conversation between Mr Turnbull and the US president in which they discussed a refugee deal struck under the Obama administration.
"The US-Australia relationship is big enough, old enough and ugly enough to cope with this snafu," Mr Rudd told CNN on Friday from Abu Dhabi.
The alliance has been around for the better part of 100 years, he said.
"I think this snafu, as I think it will be seen, will blow over and we will get back to the fundamentals of the relationship."
Mr Rudd said Australia and America have had stacks of disagreements over the years, citing his own testy and difficult times with the Bush administration over the Iraq war.
"These things come and they go," he said.
"I suppose the diplomacy of the rest of us has kind of got to get used to that."
