Mr Pence, whose visit to Sydney marked the end of a 10-day tour of the Asia-Pacific region, also confirmed the U.S. would honour a deal to accept refugees on Manus Island and Nauru, once described by President Trump as "dumb".
Under the deal, Obama agreed to take in any asylum-seekers willing to move to the United States in exchange for help closing similar USA -administered camps in central America.
One of Mr Pence's main goals during his whirlwind visit to Sydney is to smooth any ruffled feathers following the now notorious phone call between US President Donald Trump and Mr Turnbull in January.
"Let me make it clear, the USA intends to honour the agreement subject to the results of the vetting processes now applied to all refugees considered for admission to the United States of America".
Mr Turnbull thanked him for the commitment and said it spoke volumes of the integrity of Mr Trump.
Despite all that, Pence said the USA will honor the agreement to reflect the importance of the long-held alliance between the states and Australia.
His trip to Australia is the first by a senior official in the Trump administration as the USA looks to strengthen economic ties and security cooperation amid disputes in the South China Sea and tension on the Korean Peninsula.
Industry Minister Arthur Sinodinos, Trade Minister Steven Ciobo and Australia's Ambassador to the US Joe Hockey were also at the brainstorming session at Sydney's Intercontinental Hotel.
Pence's comments imply that the Trump administration has added new vetting efforts to the Obama-era agreement.
Ex-President George H.W. Bush remains in Houston hospital
In January, he missed the inauguration of Donald Trump because of a 12-day hospitalization for shortness of breath and pneumonia. Bush has a form of Parkinson's disease and uses a motorized scooter or a wheelchair for mobility.
Earlier Saturday, Pence met with Governor-General Peter Cosgrove, who said the relationship between the countries is as strong as it was since "the first time we saw each other on the battlefield in 1919".
Mr Pence on Sunday remained silent on the war of words between Australia and North Korea as he joined his family for tours of Taronga Zoo, Sydney Harbour, NSW Government House and the Opera House on the final day of their official visit.
"We have an unwavering commitment to one another and it has been the foundation of security and prosperity in the Asia-Pacific for generations", he said.
In return, Australia would resettle refugees from El Salvador, Guatemala and Honduras. But it dropped him in South Korea just in time to deliver North Korea a stern warning from the US: that "all options are on the table" when it comes to curbing the North's nuclear ambitions, and that the Trump administration will seek support from its allies to pressure Pyongyang to give up its nuclear weapons and ballistic missile programs.
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.
Pence said "If China is unable to deal with North Korea, the United States and our allies will". 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.
Also, Pence was to meet with the Australian opposition Labor Party leader Bill Shorten and with some business executives.
During his visit, Pence also made a number of cultural stops.
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