Reuters has reported interviews on Nauru were suspended because US officials were uncertain about what security checks were going to be imposed on refugees under the agreement.
But Bishop denied there had been a pause.
“My understanding is that interviewing and vetting is still taking place,” she said.
“The agreement is to be honoured by the Trump administration so I’m pleased this agreement will continue.”
A US Government source also told the ABC officials were pushing ahead with implementing the deal.
But US President Donald Trump’s executive order cracking down on refugees has caused uncertainty and slowed down the approvals process.
Trump also publicly denounced the deal and labelled it “dumb” after clashing with Prime Minister Malcolm Turnbull on the issue.
The ABC’s political reporter Stephen Dziedzic said the Australian government was convinced Trump’s furious denunciations of the agreement were aimed at a domestic audience, and that he would not abandon it completely.
White House spokesman Sean Spicer again fielded questions about the deal during his daily briefing, and said the Trump administration would honour the agreement “in some way”.
“We are going to continue to work through this. We are going to honour these commitments in some way, meaning we are going to vet these people in accordance with the agreement that happened,” Spicer said.
The White House had previously said any refugees accepted would be subjected to “extreme vetting” before being allowed into the United States.
But officials in both Australia and the US were uncertain about exactly what “extreme vetting” meant and unsure about exactly what additional security checks would be required.
Bishop said both countries were still working through the details of the agreement.
“We remain in contact with the Trump administration and our embassy in Washington is also working with US officials and we expect that vetting process would be as tough as Australia’s vetting process in terms of health and security checks,” Bishop said.
Refugee advocates said the persistent uncertainty over the deal was causing enormous anxiety on Manus Island and Nauru – and was doing further psychological damage to refugees on both islands.
Amnesty International believes Australia’s refugee deal with the United States is dead in the water, despite indications from the White House that it will honour the agreement.
Amnesty’s Pacific Researcher, Kate Schuetze, said Australia needed to resolve the situation as it was the one that failed to meet its obligations to asylum seekers in the first place.
“The rhetoric coming out of the US and from Trump is that even though he’ll comply with the letter of the deal, the practicality may mean that they settle zero people.” she said.
“The refugees cannot languish in limbo and the situation must be resolved before lives are lost,” she said.