It did not mention the refugee deal, which clashes with Mr Trump's attempts to restrict immigration from seven Muslim-majority countries deemed as terrorist threats.

Ms Bishop invited Mr Pence to visit Australia "as soon as possible" whenever he tours Asia and said she expected the President and Prime Minister to meet in person at upcoming international meetings or in Washington during this year.

The Turnbull government is eager to host a senior Trump administration member to shore up the 75-year US-Australia alliance, following US Defence Secretary James Mattis's recent visit to Japan and South Korea.

The high-level meeting between the Foreign Minister and Vice President was described by a senior official in Washington as an opportunity to "repair" relations.

Mr Trump reportedly told Mr Turnbull "this is the worst deal ever" and "this was the worst call by far" after speaking to four other world leaders including Russia's Vladimir Putin. He accused Australia of seeking to export the "next Boston bomber", according to The Washington Post, in an exchange later confirmed separately by officials in Canberra.

Mr Turnbull said earlier this month that the call ended courteously and he expressed confidence in the strength of a US-Australia alliance.

Ms Bishop and Mr Pence discussed the US-led coalition's evolving plan to defeat Islamic State militants in Iraq and Syria, she said.

The President has ordered the Pentagon to present a plan by early March to defeat Islamic State.


At this stage, Ms Bishop said the US had not requested additional Australian commitments beyond the 780 personnel currently training Iraqi soldiers, assisting with airstrikes and providing military advice on counter-terrorism.

The current deployment was "appropriate" but "always under review", she said.

The same applied to Australia's deployment to Afghanistan, where the commander of the US mission said earlier this month that coalition forces are in a "stalemate" with the Taliban and signalled that he was seeking extra coalition forces.

Iraqi forces on the weekend began an offensive to retake West Mosul from two years of Islamic State control and have gained more than 125 square kilometres of ISIS-held territory, the Pentagon said on Tuesday.

On the subject of economic relations in light of Mr Trump's vow to review all free trade agreements and renegotiate unfair deals, Ms Bishop said the 2005 US-Australia free trade accord was not raised by the Vice President.

The US has a $25 billion trade surplus with Australia and BHP Billiton is a large investor in US shale oil and gas, facts that Ms Bishop later told reporters showed the mutual benefit of the trade and to downplay any prospect of Mr Trump seeking to reopen the deal.

Ms Bishop met US intelligence agencies and spoke on the phone to members of Congress, several of whom earlier this month criticised Mr Trump's shabby treatment of Mr Turnbull.

Ambassador to the US Joe Hockey, who accompanied Ms Bishop to the meetings, described the visit as "extremely successful".

Mr Hockey this month held an emergency meeting with Mr Trump's chief of staff Reince Priebus and chief strategist Stephen Bannon, a hardliner against Muslim immigration.

Ms Bishop was scheduled to meet Secretary of State Rex Tillerson early Thursday morning Australian time.

Defence Minister Marise Payne met US Defence Secretary Mattis in Brussels last week.