Under the arrangement, agreed by former US President Barack Obama and Turnbull in November within days of Trump's election, Australia would transfer up to 1,250 refugees currently held in offshore detention centers on the Pacific Island nation of Nauru and Papua New Guinea's Manus Island to the United States. Many are from Iran.
"Let me make it clear that the United States intends to honor the agreement, subject to the result of the vetting process that has now applied to all refugees considered for admission to the United States of America," said Pence, who is in Australia as part of a 10-day Asia-Pacific tour.
"President Trump has made it clear that we'll honor the agreement, but it doesn't mean we admire the agreement," he added. "Frankly looking back at the last administration, the President has never been shy about expressing frustration with other international agreements, most notably the so-called nuclear agreement with Iran."
Pence said the decision to abide by the deal despite Trump's "reservations" was a "reflection of the enormous importance of the historical alliance between the United States and Australia."
Turnbull voiced his thanks, saying "the commitment to honor the deal is very important and one that speaks volumes."
In a tweet posted February 2, Trump made his feelings about the agreement quite clear, saying: "Do you believe it? The Obama Administration agreed to take thousands of illegal immigrants from Australia. Why? I will study this dumb deal!"
CNN's Elaine Ly contributed to this report.