Pence sought to reassure Australia Saturday that the United States remains committed to the countries' longtime alliance, following a tense first telephone call between Trump and Turnbull.
In return, Australia would resettle refugees from El Salvador, Guatemala and Honduras.
"The President and I have, in his words, great confidence that China will deal with North Korea, and I know [Australia] shares that hope", Mr Pence said.
On the second full day of his whirlwind visit Mr Pence, his wife Karen and daughters Charlotte and Audrey will visit the Sydney Opera House, Taronga Zoo and take a harbour cruise with NSW Premier Gladys Berejiklian.
Both the USA and Australia have pressured China to take more responsibility in influencing North Korea to abandon its nuclear program.
Pence and Turnbull said they are aligned in their opinion that China should use its leverage with North Korea to de-escalate the nuclear threat. The camps are where asylum-seekers were taken when halted by the Australian navy before reaching the nation's shore. Afterwards, it wasn't clear if the US would honor the deal - which Trump later tweeted was "dumb" - but on Saturday, Pence assured Australia that America would indeed accept the refugees.
Pence said "If China is unable to deal with North Korea, the United States and our allies will".
US officials have been pushing ahead with security checks of refugees on Manus Island and Nauru in recent weeks, and several arms of the US Government have insisted the agreement is still on track.
Turnbull in his remarks thanked Pence for honoring the agreement, saying it spoke to the "integrity" of Trump and his administration.
But the promise from Mr Pence is still the clearest indication from the administration's upper echelons that some refugees will actually be resettled in the U.S., although the exact number of people who will be allowed in remains unclear.
Pence said Saturday that the USA will honor the agreement even if the Trump administration doesn't agree with it.
"President Trump has made it clear that we'll honor the agreement, but it doesn't mean we admire the agreement", Pence said.
Pence said his trip to Australia during the first three months of Trump's administration and Trump's plans to travel to Asia next fall are strong signs "of our enduring commitment" to that part of the world. "And the president wanted me to, early in this administration, to reaffirm the strong and historical alliance between the United States and Australia".
Also, Pence was to meet with the Australian opposition Labor Party leader Bill Shorten and with some business executives.
"So this is a kiss and make-up trip".