The latest signals from the Trump White House have encouraged the Turnbull government’s hopes that the administration will stick to the refugee deal forged with Barack Obama despite the President’s denunciation of it.

Trump has suggested the actions of a previous administration have to be respected, while his spokesman Sean Spicer said while the President was extremely upset with the deal, he would allow the process to continue.

But Australia expects that the Americans are likely to play hardball in assessing the people from Nauru and Manus Island, which they have said will involve “extreme vetting”. This means that how many of the some 1,250 to be assessed would actually be taken by the US is an open question.

Australia’s ambassador to Washington, Joe Hockey, met Trump’s chief of staff Reince Priebus and chief strategist Steve Bannon at the White House to discuss the situation, after detail of the President’s angry words when he spoke to Malcolm Turnbull at the weekend was leaked. The White House meeting was requested by Australia.

Turnbull has remained publicly confident all week that the deal will be honoured by Trump. He received this assurance in the weekend phone call.

But subsequently there were mixed signals, and fresh doubt arose when Trump tweeted on Thursday (AET) “Do you believe it? The Obama Administration agreed to take thousands of illegal immigrants from Australia. Why? I will study this dumb deal!”

But in remarks delivered when he met a group of Harley Davidson business executives and union representatives, Trump appeared to be explaining his tweet.

He said the administration was “negotiating properly with countries, even countries that are allies. A lot of countries taking advantage of us … really terribly taking advantage of us”, he said.

“We had one instance in Australia. I have a lot of respect for Australia, I love Australia as a country. But we had a problem where for whatever reason President Obama said that they were going to take probably well over 1000 illegal immigrants who were in prisons and they were going to bring them and take them into this country, and I just said ‘why?’”

“I just wanted to ask a question.

"1250, could be 2000, could be more than that. And I said, why? Why are we doing this? What’s the purpose?

"So we’ll see what happens but a previous administration does something, you have to respect that but you could also say, why are we doing this?”, he said.

While the White House described the weekend Trump-Turnbull conversation as “cordial”, Turnbull said in a Friday radio interview that he’d say it was “frank”.

“Acting in Australia’s interests, we secured the commitment from the US President that we wanted and that we sought and we thank him for making that commitment”, he said.

Turnbull said that clearly Trump wouldn’t have done the deal himself “but we have persuaded him to stick with it nonetheless and that was the outcome that I wanted to achieve and that’s what I’ve achieved.

"And that’s my job as Australian Prime Minister, is to defend and advance our interests.

"I’m Australia’s advocate … My job is to get results for us.”

When it was put to him that Trump was a brash character, Turnbull said he was “clearly a very big personality”.

With Turnbull receiving some praise over his handling of the issue, Bill Shorten offered qualified approval.

“It would appear that Mr Trump needs to show more respect to Australia and the Australian alliance than he is doing if the media reports that we’ve got are correct. Now, I don’t think either of them have covered themselves in glory, but in this case for once, I’m more on Malcolm Turnbull’s side because Australians have to stick together”, Shorten said.

Michelle Grattan does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond the academic appointment above.