AppId is over the quota
Argentine foreign minister Hector Timerman pulled out of the meeting, due to be held in London, after representatives of the Falkland Islands government were slated to attend.
Argentina does not recognise the government as legitimate.
In a statement Mr Timerman described the islanders as the 'colonists from the Malvinas.'
Residents were widely expected to have told Argentina they should respect islanders' rights and leave them in peace.
It is believed that the majority of the 3,000 islanders want to remain under British rule.
This latest diplomatic spat is likely to further raise the tensions between the UK and Argentina over the future of the islands.
In a strong statement Mr Timerman said he was sorry that Mr Hague "can't meet without the supervision of the colonists from the Malvinas".
The curt letter added: 'It's a shame that you reject a bilateral meeting. You need not keep trying to put together meetings during my visit to London. Leave that job to our own efficient embassy.'
Mr Timerman invited Mr 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".
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.
In a statement released before Mr 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 Mr 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 Mr Hague."
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."
