Security and North Korea especially dominated talks between the Vice President and the Prime Minister, subjects that provided plenty of common ground to reaffirm a bi-lateral relationship that had showed strain soon after President Trump's election.

"The eyes of the world are on Beijing," Mr Turnbull said at a press conference following high-level bilateral talks at Admiralty House in Sydney on Saturday. "We seek leadership from China to join the leadership shown by the United States and Japan and Australia.

"We call on China to make that stronger commitment to ensure North Korea stops this reckless and dangerous conduct."

Mr Turnbull said China had the "responsibility" and a unique ability and leverage to rein in the rogue state's increasingly threatening rhetoric and military provocations.

The Australian-US position on the troubled peninsula has not gone unnoticed.

Last night North Korea reportedly accused Australia of "blindly toeing the US's line" and warned of a possible nuclear strike if it persisted.

ABC online quoted a North Korean Foreign Ministry spokesperson as saying, "If Australia persists in following the US's moves to isolate and stifle North Korea... this will be a suicidal act of coming within the range of the nuclear strike of the strategic force of North Korea."

North Korea had inflamed tensions with an attempt to test fire a missile last Sunday that put the world on high alert and drew condemnation from the UN Security Council.

There has also been speculation North Korea may be seeking to perform an underground nuclear test.

"President Trump and I are truly grateful, truly grateful, to you for calling on China even this week to play an even more active and constructive role," Mr Pence said.

Mr Turnbull sidestepped a question about whether Australia would ever join possible future military action against North Korea and said Australia's commitment was focused on public and private diplomacy.

But Mr Pence reiterated an ultimatum US President Donald Trump had first issued via Twitter: "If China is unable to deal with North Korea the United States and our allies will."

But both leaders expressed confidence that China would act to help secure a long-standing regional aim of securing a nuclear-free Korean peninsula.

Mr Pence said he was encouraged by the signs of Chinese progress in negotiations with North Korea but he did make reference to the President's recent escalation of the situation.

President Trump was recently criticised for an apparently exaggerated boast that he had sent an "armada", including naval carrier the USS Carl Vinson, as a warning to North Korea.

Mr Pence confirmed the ship was yet to take position in the Sea of Japan but said it would arrive in coming days.

The two leaders also discussed economic relationships.

Mr Turnbull declined to criticise the President's decision to withdraw from the Trans-Pacific Partnership Agreement, of which Australia is a part, in favour of focusing on deepening bilateral trading relationships.

As an "international businessman", Mr Turnbull said, his American counterpart was not blind to the benefits of free trade.

Total Australian economic dealings with America have grown by 50 per cent in the past three years, the Vice-President said, and were now worth $1.5 trillion.

America is Australia's second-largest trading partner.

Mr Pence said his visit was designed to reaffirm the strength of Australia's partnership with America, which he said was based on security and prosperity.

Relations between the two nations had showed strain early this year after an apparently testy phone call between the Prime Minister and American President who pushed back on a refugee resettlement deal.

But Mr Pence confirmed the deal would be honoured.

"The decision can be seen as a reflection of [Australia's] enormous importance," he said.

Mr Pence will later meet with Opposition Leader Bill Shorten, business leaders and NSW Premier Gladys Berejiklian.