Donald Trump has said the United States’ position on the Falkland Islands is “one of many” under review, as he pressed the UK to increase military spending.

The US president said the UK has “got some problems, but they’ll get solved” when asked about defence funding as a follow-up question to his response on the Falklands.

It comes after The Daily Telegraph reported, external US defence officials were drawing up proposals to incentivise Nato allies to meet their spending pledges, with a threat to oppose UK sovereignty over the Falklands among the possible options.

The UK government responded by saying Falkland islanders “are British with a right to determine their own future”.

A spokesperson added: “The islanders have repeatedly expressed their wish to remain a British overseas territory and our commitment to them is unwavering.”

The Falkland Islands, in the south-west Atlantic Ocean, remain the subject of a sovereignty dispute between Britain and Argentina.

The two countries waged a brief but bitter war over the territory in 1982. A British military task force ejected Argentine forces, which had landed on the Falklands to stake a territorial claim.

The 74-day conflict led to the deaths of 255 British military personnel, three islanders and 649 Argentine military personnel.

Previous US administrations have formally recognised the UK’s de facto administration of the islands, but have not taken a formal position regarding sovereignty.

Speaking to reporters on Monday, Trump was asked by the BBC if he was reviewing the US position on the Falkland Islands.

The president replied: “I always review every position. That’s just one of many.”

Trump’s remarks were labelled “nonsense” by Labour MP Dame Emily Thornberry, who chairs the Commons foreign affairs committee, as she asked the UK government to issue an official response in the House of Commons.

Foreign Office Minister Uma Kumaran replied: “The UK has no doubt about its sovereignty over the Falkland Islands.

“They are and will always remain a British overseas territory in line with the wishes of the Falkland islanders.

“The UK is steadfast in our support for the islanders’ rights of self-determination.”

Kumaran said she had seen Trump’s comments, adding: “Our position remains unchanged.”

In April, an internal Pentagon email reported by Reuters suggested the US was considering options to punish Nato allies it believed had failed to support its war in Iran.

The options reportedly included the prospect of the US reviewing its position on Britain’s claim to the Falklands.

Reports of this proposal have re-emerged in recent days in relation to defence spending.

Prime Minister Andy Burnham has said he will honour a commitment made by predecessor Sir Keir Starmer to devote 3.5% of UK gross domestic product (GDP) on core defence spending by 2035.

On Tuesday, Chancellor John Healey told The Times, external he would “set out a clear path” to meeting that Nato pledge at the next government spending review, expected in the spring of next year.

He added that this would also include a target date for increasing spending to 3% of GDP.

Healey resigned as defence secretary in Sir Keir Starmer’s government following a row over military spending.

His resignation letter in June expressed his frustration that the government had no clear timetable to hit the 3% spending target, which he believed should happen by 2030.

The UK government has also faced questions over whether it will continue with a deal to hand over the Chagos Islands to Mauritius and pay to lease back the joint US-UK military base on Diego Garcia.

It was confirmed in April that the deal had been paused indefinitely because of Trump pulling his support.

Kumaran told MPs on Tuesday that “maintaining long-term operational control and security of the base remains a top priority and is the entire basis for the UK-Mauritius agreement.”

The minister also said funding for the treaty would be provided for “within the existing spending review settlements” for the Foreign, Commonwealth and Development Office and the Ministry of Defence.

Conservative shadow defence secretary James Cartlidge criticised the remarks and said the deal “belongs on the ash heap of history”.

He said in a statement: “Burnham should show some backbone and break with this terrible legacy of the Starmer years by ditching his crazy Chagos deal once and for all, and spending the savings on our armed forces.”

In the Commons, Conservative shadow Foreign Office minister Wendy Morton noted Sir Keir’s administration acknowledged in April that the Chagos treaty had become “impossible to agree at political level” and asked what had changed.

Kumaran said the Burnham government would “continue to work with the US and Mauritius to find a way forward that is in the UK’s best interests and protects our national security”.

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