Malcolm Turnbull appears set to meet Donald Trump in New York next week

Malcolm Turnbull appears set to have his first face-to-face talks with Donald Trump next week after meeting the US vice-president, Mike Pence, at the weekend, and the US defence secretary, James Mattis, in Afghanistan before Anzac Day commemorations.

Turnbull, during a lightning visit to Australian troops in Iraq and Afghanistan, said he looked forward to continuing the discussions he had undertaken with Trump administration officials with the president “at an early opportunity”.

The prime minister is understood to be awaiting an official invitation to an event in New York on 4 May commemorating the 75th anniversary of the battle of the Coral Sea, which the president may turn into a leaders’ gathering.

As well as hinting that a trip to the US was imminent, Turnbull did not rule out making a larger contribution in Afghanistan and Iraq if the US requested it, signalling that Australia may build on a training role.

“There is no doubt that in both theatres, there is going to need to be a long-term commitment,” the prime minister told reporters on Tuesday.

“But it is one of supporting, above all of training, the Afghan and Iraqi security forces, both military and police, to ensure that they have the ability to defend their own country, to push back the terrorists where they’ve made gains and to secure the territory that the government is holding.

“So it is going to be a long-term commitment and we’ll consider, with our allies, in these conflict areas, we’ll consider requests for further support. As it evolves, we’ll be looking at that.”

If the New York trip proceeds, it will be the first meeting between Turnbull and Trump since an infamous phone call when the newly elected US president upbraided the Australian prime minister over the refugee resettlement deal negotiated with the Obama administration.

Despite the bruising encounter, the US has indicated it will proceed with the deal. During his visit to Sydney, Pence said the US would honour the agreement even though the new administration did not approve of it.

“President Trump has made it clear that we’ll honour the agreement,” Pence said at the weekend.

“That doesn’t mean we admire the agreement. Frankly, looking back on the past administration, the president has never been shy about expressing frustration with other international agreements.”

If the New York meeting doesn’t materialise, the two leaders will have an opportunity to meet at the G20 summit in Germany in July.