Australia and the United States struck a deal last year for refugees in offshore detention camps on Papua New Guinea's Manus Island and Nauru to be resettled in the United States.
But with the Democrats voted out of power, there was uncertainty about whether newly-elected Republican President Donald Trump would honour the agreement.
Over the weekend, the Prime Minister Malcolm Turnbull said he received confirmation it was going ahead.
He has reiterated the statement.
"The Trump administration has committed to progress with the arrangements, to honour the deal - if you like - that was entered into with the Obama administration and that was the assurance the President gave me when we spoke on the weekend."
In a briefing, White House spokesman Sean Spicer said more than 1,000 refugees being considered for resettlement would be subject to what he called 'extreme vetting' by US authorities.
"Those people - part of the deal is that they have to be vetted in the same manner that we're doing now. There will be extreme vetting applied to all of them. That is part and parcel of the deal that was made."
Prime Minister Turnbull says Australia has similar measures in place.
"The US government's vetting, security and other vetting is very, very rigorous and always has been rigorous and it's understandable and to be expected that a new administration would want to make sure that it was very, very rigorous. We don't cut corners or compromise on keeping Australians safe and the United States government has exactly the same attitude so, vetting will always be rigorous that's always been part of the agreement."
Now the ABC is reporting its Washington bureau has received a follow-up call from the White House to say President Donald Trump is still considering whether to uphold the refugee swap deal.
SBS News is seeking independent clarification from the US government.
Refugee advocates in Australia, meanwhile, say the delays are creating more anxiety for detainees awaiting an outcome.
The Refugee Council of Australia says they should be brought to the mainland.
The federal opposition leader Bill Shorten has urged the prime minister to be honest with the Australian people about the future of the agreement.
"I absolutely hope the deal goes ahead, absolutely. Mr Turnbull said that Mr Trump's promised the deal will go ahead so I assume that Mr Turnbull was being straight with us. I think it would be helpful if my opposite number just told people what's really going on."
