The UK has insisted the Falkland Islands are British after Argentina broke a co-operation deal and pushed for talks on the islands' sovereignty.
In 2016, both sides agreed to disagree on the sovereignty of the Falklands in favor of improved relations.
Argentina pulled out of the pact this week and informed UK Foreign Secretary James Cleverly.
The Falkland Islands were subject to a bloody war in 1982 when Argentina tried to stake a territorial claim.
In response, Mr Cleverly tweeted: "The Falkland Islands are British.
“Islanders have the right to decide their own future - they have chosen to remain a self-governing UK Overseas Territory."
The 2016 agreement between Argentina and the UK pledged to "improve co-operation on South Atlantic issues of mutual interests".
Mr Cleverly was informed about the decision by his Argentinean counterpart Santiago Cafiero when the pair met at the G20 summit in India earlier this week.
Mr Cafiero called for talks on the sovereignty of the Falkland Islands, known in Argentina as the Malvinas.
The UK's minister for the Americas, David Rutley, said it was a "disappointing decision" after he had had a "constructive visit" to Buenos Aires.
"Argentina has chosen to step away from an agreement that has brought comfort to the families of those who died in the 1982 conflict," he said.
The Falkland Islands are a British overseas territory in the south-west Atlantic Ocean. Argentina has long claimed sovereignty over the islands.
Argentina invaded in 1982 in a bid to reclaim sovereignty and said it had inherited the Falkland Islands from Spain in the 1800s.
A brief but bitter war lasting 74 days followed - with 655 Argentinian, 255 British and three Falkland casualties - before British forces regained control on 14 June 1982.
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