US President Donald Trump once called the deal, which was agreed under his predecessor, "dumb".
The agreement allows for up to 1,250 asylum seekers to Australia to resettle in the US.
The agreement would be honoured, but not necessarily admired, visiting Vice-President Mike Pence said after talks with Australian PM Malcolm Turnbull.
Mr Pence was speaking at a joint press conference with Mr Turnbull.
Australia has controversially refused to accept the refugees, most of whom are men from Iran, Afghanistan and Iraq, and instead holds them in offshore detention centres on the Pacific nations of Nauru and Papua New Guinea.
In the first two weeks of his presidency, Mr Trump said he had a bad phone call with Mr Turnbull, when the Australian filled him in on the deal.
Mr Turnbull later said he was disappointed that details of the call had been made public.
- Trump in 'worst call' with Australia PM
Relations appear to have warmed significantly since then.
The news conference between Mr Pence and Mr Turnbull was, aside from that one awkward topic, largely characterised by mutual praise.
Mr Pence spoke at length about military collaboration with Australia, and stressed the need to ensure stability on the Korean peninsula.
As tension with North Korea continues, he also used the occasion to announce that a US naval strike group would arrive in the Sea of Japan in days.
Mr Pence said: "The one thing that nations, most especially the regime in North Korea should make no mistake about, is that the United States has the resources, the personnel and the presence in this region of the world to see to our interest and to see to the security of those interests and our allies."
However, there had been confusion as to the whereabouts of the US carrier group, with contradictory statements from Washington.