Foreign Secretary William Hague invited Hector Timerman to a meeting when he visits London next week to discuss issues relating to the islands, which Argentina still claims.
The offer was rebuffed by Mr Timerman on the grounds that members of the Falklands Islands government, which Buenos Aires refuses to recognise, would be present.
A Foreign Office spokesman said: “We note that Mr Timerman has publicly rejected the Foreign Secretary’s offer of a meeting whilst he is in the UK.
“We have always said that we are open to discuss a wide range of issues that affect our two countries, including our respective interests as members of the United Nations Security Council.
“However, it is clear from Mr Timerman’s plans in the UK that the Falkland Islands are already on his agenda.
“We remain concerned about the Argentine government’s behaviour towards the Falkland islanders, so it is right and proper that they are involved in the part of the meeting that concerns the islands.
“We have made that clear to the Argentine government in recent exchanges, and the Foreign Secretary’s offer of a meeting on these terms still stands.”
In a statement last night, Mr Timerman said he was sorry that Mr Hague was unable to meet “without the supervision of the colonists from the Malvinas” – the Argentine name for the islands and invited Mr Hague to meet him in Buenos Aires.
Argentine president Cristina Fernandez de Kirchner has in recent years strongly asserted her country’s demands for the Falklands despite the opposition of the islanders.
Prime Minister David Cameron has repeatedly insisted the residents of the Falklands must decide their own future and a referendum on the islands’ political status is to be held in March.