Fresh from bilateral talks with Prime Minister Malcolm Turnbull, the visit represented a lighter side to Mr Pence's weekend trip to Australia.
Part of Mr Pence's mission while in Australia is to smooth any ruffled feathers caused by Mr Trump who blasted Mr Turnbull over an asylum seeker settlement plan during their now notorious phone call shortly after Mr Trump's inauguration in January.
"We are very honoured you are visiting us here so early in the term of new Trump administration", he said.
Mike Pence reassured Australian Prime Minister Malcolm Turnbull that the U.S. would hold up its share of an agreement stuck by the Obama administration, even if it did not "admire" the deal.
Given President Trump's unpopularity with many Australians, Mr Turnbull has been urged by some to distance the country's relationship with the United States in favour of stronger ties with China.More news: Gold Prices Remain High as French Election Nears
In return, Australia would resettle refugees from Guatemala, Honduras and El Salvador, according to Reuters news agency, as part of a US-led program in Central America.
Tensions over North Korea's nuclear ambitions were also discussed by the pair during their meeting, with both agreeing that China should use its leverage with Pyongyang to peacefully de-escalate the threats posed by Kim Jong-Un's missile programme.
"We will honor this agreement out of respect to this enormously important alliance", Pence told a joint news conference with Australian Prime Minister Malcolm Turnbull in Sydney.
Mr Pence said the United States believes it will be possible to achieve its objective of ending North Korea's nuclear program peacefully, largely with the help of China.
The fallout over the deal has strained the typically cozy alliance between the US and Australia. Though Turnbull has repeatedly rejected calls for Australia to choose between the superpowers, some critics of Trump have urged Australia to align itself more closely with Beijing.More news: Trump's cybersecurity review misses deadline
Under the deal, agreed with former President Barack Obama late past year, the US would resettle up to 1,250 asylum seekers held in offshore processing camps on South Pacific islands in Papua New Guinea and Nauru. Australia is the only country to have fought alongside the U.S.in every major conflict since World War I.
The alliance was front-and-center for Pence in his meetings with top Australian officials, who repeatedly noted their military partnership for almost a century.
Earlier on Saturday, Mr Pence met Australia's governor general Peter Cosgrove, who said the relationship between the countries was as strong as it was since "the first time we saw each other on the battlefield in 1919".
Mr Pence said the TPP was a "thing of the past" for the US. Pence and his family are also scheduled to tour the Sydney Opera House and other landmarks.
He will also meet Opposition Leader Bill Shorten, and host a gathering of American business leaders.More news: Afghan Army base attack death toll rises to 140?
"(What) 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 interests and to see to the security of those interests and our allies", he said.
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