The federal government had previously denied there was a swap of people involved in the deal between the two countries.
However, Immigration Minister Peter Dutton has suggested to Sky News that Australia will not take the asylum seekers from Central America unless the United States keeps its promise.
(Dutton:) "We wouldn't take anyone until we had assurances that people were going to go off Nauru and Manus."
(Reporter:) "Oh, right, so it's quid pro quo -- first we lose people, and then they come?"
(Dutton:) "Well, we want an outcome in relation to Nauru and Manus. That's the most important thing. My job is to argue our case, the US can argue theirs."
And when Mr Dutton was pushed again for clarification, he responded:
"One of the lessons that we've learnt from past arrangements - say, the Malaysia deal, for example, that Julia Gillard entered into - we accepted all the people from Malaysia, not one person went from Australia. So, we're not going to be sucked into that sort of a silly outcome."
Opposition defence spokesman Richard Marles has told Sky it is just another example of the Government's lack of transparency.
"He made it clear that it was contingent, that taking people from Costa Rica was contingent on America taking those from Manus and Nauru. And so, clearly, this was a deal ... quid pro quo, one for the other. That is what happened last year. That's evidently what occurred. And yet we've got a Government that's been denying that from day one."
But it appears there is dissent within the Coalition about the deal.
Foreign Minister Julie Bishop, meeting with Trump administration officials in Washington, denies it is a people swap deal.
"That's not the way I would categorise it. Australia is a very generous nation when it comes to resettling those who are found to be refugees from all over the world, and we'll continue to do so. We are seeking to resettle a number of people who came via the people smuggling trade and have been in Nauru, in particular, with the United States, but we will continue to take refugees from across the world as we've always done."
Immigration Minister Peter Dutton told Sky News the asylum seekers from Costa Rica will be assessed on a case-by-case basis.
"Some of the examples that I've been given are Christians who are fleeing that part of the region trying to escape gang violence, and so we will look at those individual cases. If we determine that they're refugees, then we can take them. If we think they're not, again, it's our sovereign right. But I won't be taking in people who I think are a risk to our national security or would detract from our community."
He says, while he believes the first transfers from Manus and Nauru will get underway in a couple of months, the United States will take the process seriously.
"We decide who comes to our country, and we're very serious about that, because the US wants to exert the same sovereignty. So they'll look at the individual cases, they'll make the ultimate decision, but it's working well and we've got a very good relationship with the people from State and Homeland Security and I'm confident we can get people off Manus and Nauru as quickly as possible."
Julie Bishop has revealed little on the matter, despite meeting with US vice president Mike Pence.
She says Australia's offer to resettle Costa Ricans was not discussed, and she remains tight-lipped on a transfer time frame.
"The matter is being dealt with at officials level, and the agreement is still being progressed."
