Scott Morrison insists Australia will not be drawn into any military conflict with Iran, declaring our commitment is limited to protecting freedom of navigation in the Strait of Hormuz.

Donald Trump, who flagged the prospect of a military strike against Iran, including, possibly, with nuclear weapons, during a meeting with Morrison in the Oval Office, before backtracking and saying his preference was for restraint – has sent additional troops and enhanced air and missile defence systems to Saudi Arabia and the United Arab Emirates in response to a drone attack on Saudi oil facilities on 14 September.

Trump is expected to use the looming opportunity of leaders week at the United Nations to try to cajole other nations into participation. Trump is scheduled to meet at least a dozen world leaders during his three days in New York.

Morrison told travelling reporters after a reception at the private residence of Australia’s ambassador to Washington that Australia was engaged in the Strait of Hormuz and “that’s where our involvement is”.

“There was no discussion about anything else. There was an appreciation of our involvement in that particular operation, which I remind everyone is about freedom of navigation in the Straits of Hormuz,” the prime minister said.

“That’s what that is about. The other matters that are being pursued by the United States are matters that they’re pursuing, and I made it very clear when we announced our involvement in [the Strait of Hormuz] that it was very much about that freedom of navigation issue and that’s what it is about and that’s appreciated.”

Morrison said he had discussed arrangements for the freedom of navigation exercise with the US defence secretary, Mark Esper during his meetings with members of the Trump cabinet on Friday Washington time.

Morrison praised Trump’s restraint on Iran. “I made a point of commending the president yesterday on what I understand to be his natural instinct of restraint on these matters and he said that I think fairly plainly yesterday in the Oval Office I think there is an instinct towards restraint from the president and I commended him for that, and it was good to have the opportunity to confirm that again in the course of our discussions.

“I mean Australia will make its decisions in our national interest. I said at the press conference yesterday that where we’ve worked together it’s because we have shared objectives,” the prime minister said.

“It’s not because [America] asks us to do this, or we ask them to do that, it’s because we share objectives and where those objectives are shared then you can expect an alignment of activities and operations.”

Morrison said people needed to avoid “getting ahead of themselves” about what Trump might or might not do in relation to Iran. He said these issues were “dealt with I think in a very iterative way and I think that’s what you’re seeing”.

Trump told reporters during his meeting with Morrison that he could launch a military strike on Iran “right here”.

“It’s all set to go. I could do it right here and then you’d have a nice big story to report,” the president declared. But moments later he suggested holding off was the better course of action. “I think the strong person’s approach, and the thing that does show strength, would be showing a little bit of restraint.”

Morrison wound up his Washington program on Saturday local time with a $150m commitment to support Nasa in launching expeditions to the moon and to Mars, and with a visit to a centre helping veterans to become entrepreneurs. He then attended a soiree at the ambassadorial residence with Trump administration officials and Australian business figures including Gina Rinehart, Anthony Pratt and Kerry Stokes.

Morrison will travel with Trump to Ohio on Sunday local time to open a box factory owned by Pratt, the Australian billionaire box maker. That event will also be a campaign rally for Trump.

The prime minister will then fly on to Chicago, where he will give a keynote speech, before heading to New York and the United Nations.