Representatives of the Falkland Islands government were flying to London this weekend to tell Hector Timerman that Buenos Aires should respect islanders' rights and leave them in peace.
But Timerman, who had initially asked for a one-to-one meeting with the Foreign Secretary, last night said he would not accept the offer of a meeting involving the Port Stanley government, which Argentina does not recognise as legitimate.
The United Nations regards the dispute over the islands, which Argentina knows as the Malvinas, as a bilateral issue between Buenos Aires and London, he said.
In an open letter to Hague, Timerman said: "I lament your letter of yesterday stating you cannot meet without the supervision of the colonists from the Malvinas," using the Argentine term for the islands.
Timerman invited Hague to meet with him in Buenos Aires, where he said "my fellow foreign ministers can freely meet with whomever they wish without being pressured or having their presence conditioned on meetings that they haven't asked for and don't interest them".
Argentine president Cristina Fernandez de Kirchner has in recent years strongly asserted her country's demands for the Falklands to come under its sovereignty despite the opposition of the islanders.
Earlier this month, she had an advert published in British newspapers claiming that Argentina had been stripped of the islands in "a blatant exercise of 19th century colonialism".
In a statement released before Timerman turned down the meeting, the Legislative Assembly of the Falkland Islands stressed that their representatives, Dick Sawle and Jan Cheek, would not be "negotiating any deal".
"Rather we are anticipating a full and frank exchange of views," the assembly said.
"Indeed we look forward to giving Timerman some very direct messages on the unacceptability of Argentina's actions against the Falkland Islands in recent years.
"We demand that our rights be respected, and that we be left in peace to choose our own future and to develop our country for our children and generations to come.
"It is only right that he should hear this directly from us, as well as from Hague."
In its statement, the Falklands assembly cited Britain's opposition to "any negotiations over the sovereignty of the Falkland Islands unless and until the Falkland Islanders so wish".
"The Falkland Islands Legislative Assembly believes that the result of the forthcoming referendum will demonstrate definitively that we do not. Should the issue of sovereignty be raised at the meeting, it will not be discussed," it said.
"Members of the Legislative Assembly made it clear in their letter of 2012 to President Fernandez de Kirchner... that the Falkland Islands Government is willing to meet with the Government of Argentina in order to make our views clear, and to discuss matters of mutual interest including fisheries and communication."
A Foreign Office spokeswoman said: "We are aware that Argentine foreign minister Hector Timerman is due in the UK next week, and have invited him to come to the Foreign Office to meet the Foreign Secretary and representatives of the UK Government and the Falkland Islands Government."
Britain and Argentina fought a three-month conflict in 1982 over the sovereignty of the islands.