Pence in Sydney confirmed that the process for carrying out the deal had been initiated and would be subject to the same vetting processes that now applies to all refugees headed to the US.
Speaking on Sunday, Dutton said there was "no evidence" US authorities were holding up the deal.
"The reports I get back certainly indicate that people are engaging very well. There's no stalling and no game playing and I think that the Vice-President's words will be honoured, as you would expect and we're very grateful for that," he told ABC television.
It remains unclear how many refugees would be resettled under the plan, with US Homeland Security officials reportedly travelling to Nauru and PNG's Manus Island to do security interviews in recent weeks.
In the Insiders interview, Dutton also reiterated claims that the recent violence on Manus Island was linked to asylum seekers leading away a five-year-old boy near the facility.
"The briefing I've had is particularly succinct and clear," Dutton said.
PNG police have previously said that Dutton claims refer to an unrelated incident.
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