The UK foreign secretary, David Cameron, has suggested the Aukus pact and Nato alliance must get into “the best possible shape” to increase their chances of surviving Donald Trump’s potential return to the White House.

Speaking after high-level talks in Australia, Cameron was careful to avoid criticising the former US president and presumptive Republican nominee for 2024, saying it was “up to America who they choose as their president”.

“What we will do, as I am sure an Australian government would do, is work with whoever becomes the president,” Cameron told reporters in Adelaide, South Australia.

But Cameron appeared to implicitly acknowledge the risks that Aukus and Nato might face in the event of a second Trump presidency, by calling for efforts to ensure both were seen by the next president as well-functioning.

Cameron described the Aukus partnership – which will see the US and the UK help Australia to acquire nuclear-powered submarines – as “an absolutely brilliant arrangement” and Nato as “the most successful defensive alliance in history”.

“The best thing we can do is to get those alliances, to get those projects into the best possible shape, so whoever is the new president can see that they are working with a very successful set of arrangements,” Cameron said.

The Australian deputy prime minister and defence minister, Richard Marles, endorsed Cameron’s comments.

“We feel confident given what we have seen particularly over the course of the last few months in Congress that the Aukus arrangements really do enjoy support across the political spectrum in the United States,” he said.

“We move forward with complete confidence about what the future will hold.”

The comments were in response to a question about whether the election of Trump in November would affect the Aukus agreement that was sealed with the Biden administration last March.

Under the deal, the US will share sensitive nuclear technology with Australia and sell it at least three Virginia-class submarines in the 2030s.

Australia and the UK eventually plan to build and operate a new class of submarine to be called SSN-Aukus.

Trump has not expressed any hostility to the Aukus deal to date, although he has been highly sceptical about Nato, particularly over its members’ performance against a pledge to spend at least 2% of gross domestic product on defence.

During a stump speech in February, Trump recalled telling an unnamed European leader that he would “not protect” any Nato member that was “delinquent” and he would encourage Russia to “do whatever the hell they want”.

Cameron and the UK defence secretary, Grant Shapps, were in Australia for annual talks with their Australian counterparts on Friday.

The Australian foreign minister, Penny Wong, said Aukus was “good not just for Australia, but for Britain and the United States”.

“We will make sure it does happen,” Wong said. “We do that understanding the scale of the enterprise, the scale of the task.”

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The Australian government is facing domestic criticism after confirming it would send A$4.6bn (£2.4bn) to the UK over the next 10 years to expand the Rolls-Royce nuclear reactor production line in Derby.

The figure, while previously unpublished, is understood to come from within existing Aukus funding. The government last year indicated that the Aukus project would cost $50bn to $58bn in the first 10 years of the plan.

The Greens’ defence spokesperson, David Shoebridge, said it was “an extraordinarily bad deal and a bad day for Australian taxpayers”.

Marles said the nuclear reactors for Australia’s submarines would be made at the Rolls-Royce plant and it was “completely appropriate” to fund an increase in production.

Friday’s meeting also covered the humanitarian crisis in Gaza, the Russian invasion of Ukraine and China’s “destabilising activities” in the South China Sea.

“We know how many hundreds of thousands of Palestinians are starving,” Wong told reporters.

In a joint statement issued afterwards, Australia and the UK called on Israel to “allow immediate, safe, unimpeded and increased humanitarian relief to reach Palestinians in Gaza”.

“Given the large number of displaced persons taking refuge in the area and lack of safe spaces in Gaza, ministers shared deep concern at the potentially devastating consequences for the civilian population of an expanded Israeli military operation in Rafah,” the statement said.

Australia and the UK also “expressed the urgency of an immediate cessation of fighting in Gaza to allow aid to flow and hostages to be released as a crucial step toward a permanent, sustainable ceasefire”.

The ministers discussed how recognition of a Palestinian state “might assist in giving momentum toward” a two-state solution, but the statement did not give any detail about the timing of such a move.