Downing Street had earlier insisted the sovereignty of the Falklands was "not in question".
That came after an internal Pentagon email set out options for President Donald Trump's administration to punish NATO allies for refusing to join the US-Israeli strikes against Iran.
The memo, first reported by Reuters, suggests reassessing US ‌diplomatic support for "imperial possessions" such as the Falklands.
Argentina has long claimed sovereignty over the Falkland Islands and invaded them in 1982 before being defeated in a short but bloody war.
Downing Street said the UK's stance on the Falklands was not going to change.
"The Falkland Islands have previously voted overwhelmingly in favour of remaining a UK overseas territory, and we've always stood behind the islanders' right to self-determination and the fact that sovereignty rests with the UK," a spokesman for Starmer said on Friday.
"The question of the Falkland Islands and the UK's sovereignty and the islanders' right to self-determination is not in question, and we've expressed that position clearly and consistently."
Argentinian Foreign Minister Pablo Quirno posted on X in response: "The Argentine Republic once again expresses its willingness to resume bilateral negotiations with the United Kingdom that will allow for finding a peaceful and definitive solution to the sovereignty dispute and bring an end to the special and particular colonial situation in which they are immersed."
The Falkland Islands government said it had "complete confidence in the commitment made by the UK Government to uphold and defend our right of self-determination".
The row is the latest sign of the strains in the US-UK relationship as the King and Queen prepare for their state visit on Monday.
Downing Street said it was confident the trip would "showcase the very best of the UK-US bilateral relationship".
Falklands war veteran Simon Weston said he hoped the King would be able to get the US to "calm down".
Asked what message he hoped Charles would deliver to Trump, he told BBC television: "I would hope that he would just kind of get him to back down and calm down over the Falklands.
"What we don't need is Mr Millei to raise his sleeves and believe that aggression may work because that would just cost more lives."
The US president is an ally of Argentinian President Javier Milei, while his relationship with Starmer has deteriorated dramatically since the start of the Iran crisis.
The prime minister has refused to give the US free rein in its use of British military bases to conduct the bombing campaign against Iran.
Limited permission was granted for bases - including RAF Fairford in Gloucestershire and Diego Garcia in the British Indian Ocean Territory - to be used in defensive actions against Iran's missile sites and installations threatening the Strait of Hormuz, but only after Tehran's retaliatory actions began.
