The Foreign Secretary said claims from Argentinian counterpart Hector Timerman that the Falkland Islands would be controlled from Buenos Aires within 20 years, was "fantasy."
He added: "We shall never negotiate about the sovereignty of the islands, unless the islanders wish it."
On a visit to London last week Timerman refused to attend a meeting with the Foreign Secretary because representatives of the islanders were present.
Timerman told reporters at the Argentine ambassador's residence that as far as Buenos Aires was concerned, Falkland islanders do "not exist".
But Hague told The Sun: "This is a community that is nearly 200 years old. They seem very determined to remain British.
"If there's any chance they would change their minds, the approach by Argentina is completely counterproductive.
"It only fortifies the islanders' determination to stay British. It is only going to add to the decades and centuries that the Falklands will remain British."
The islanders will vote in a referendum next month which is expected to underline their determination to remain a British overseas territory.
The Foreign Secretary said: "Timerman made a couple of extraordinary statements, one of which was that Falkland islanders don't exist.
"I can tell him they very much do exist and they are in good heart and great shape.
"I met two members of their assembly a few days ago and they, like us, are determined about their future. It was a pity he wasn't here.
"He had asked to see me and I was happy to meet him. But in any discussions about the Falklands, the islanders will always be present."
Hague said the current Argentine government, led by president Cristina Fernandez de Kirchner had turned away from a process of diplomatic dialogue "into a pattern of bullying and intimidatory behaviour towards the Falkland Islands".
He said: "It would be better to talk to the islanders rather than deny their existence or claim Argentina will have the islands within 20 years. These things are fantasy.
"It would be far better for their country to be realistic about these things and deal with a free people."