The Falklands Islands will be under Argentinian control within 20 years, the South American country's foreign minister, Héctor Timerman, has said in an interview with the Guardian.

Visiting London for the first time, he ruled out a military solution to the 130-year-old sovereignty dispute but claimed the world increasingly recognised that the islands were a product of colonialism. He accused the British government of being motivated by a fanatical desire to hold on to the islands and claimed "the United Kingdom has never missed an opportunity to miss an opportunity to find a solution for the Malvinas".

He said: "I don't think it will take another 20 years. I think that the world is going through a process of understanding more and more that this is a colonial issue, an issue of colonialism, and that the people living there were transferred to the islands."

He vowed that the interests of the existing islanders would be protected under Argentinian rule, including "their way of life, their language and right to remain British citizens". But he drew a distinction between the islanders' interests, which could be met, and their wishes, which could not.

Timerman is in London to argue the historical and legal case for Argentinian sovereignty over the islands. He has refused to meet the foreign secretary, William Hague, after the Foreign Office insisted representatives of the islands also attend. He said Hague's refusal to hold talks bewildered him as in the past the British had been quite willing to talk to a military junta that claimed 35,000 Argentinian lives.

In his interview, Timerman refused to discuss the possibility of joint sovereignty, saying he would not as a diplomat conduct negotiations through the Guardian and could only do so directly with Hague.

Explaining his refusal to meet the islanders, Timerman, speaking at the Argentinian embassy in Mayfair, said: "We have been trying to find a peaceful solution for 180 years. I think the fanatics are not in Buenos Aires [but] maybe in the United Kingdom because they are 14,000km away from the islands. And I think they are using the people living in the islands for political [reasons] and to have access to oil and natural resources which belong to the Argentine people. I think we are not fanatical at all.

"There is not one single country in the world which supports the right of the United Kingdom to govern over the Malvinas. Not one.

"According to the United Nations, there are only two parties to the conflict – the United Kingdom and the Republic of Argentina. It is an issue that has to be resolved by Argentina and the United Kingdom. By introducing a third party [the Falkland Islanders], the United Kingdom is changing more than 40 resolutions by the United Nations, which call on the two countries to negotiate."

Asked if it would be better to develop a relationship with the islanders as a way of reaching a settlement, he said: "I don't have to persuade them. The United Nations says there is a conflict between the United Kingdom and Argentina. I don't have to persuade anybody. We have to apply international law and accept the resolutions, if not the UN becomes a body that is only useful when it backs the powerful."

He also dismissed the referendum that is being held by the British government on the islands in March, designed to underline that the islanders want to remain part of the British Overseas Territories. He said the referendum "is something that doesn't mean anything because if you ask the colonial people who came with a colonial power and replaced the people who were living in the islands, it is like asking the British citizens of the Malvinas Islands if they want to remain British".

He likened it to asking only new Jewish settlers in the Occupied Territories if they want to remain Israeli.

He pointed out that the number of islanders who have lived there for more than nine generations was tiny.

Expressing his country's deep sense of grievance, in the interview jointly conducted with the Independent, Timerman added: "It is strange to be accused of being fanatical when you see all your natural resources being taken away, part of your country under the administration of a foreign power and you try to sit down and have dialogue and you are refused."

A form of joint sovereignty has been repeatedly urged on both countries as the best solution to the conflict, and in the past before the invasion of the islands by the military dictatorship in 1983, British diplomats had discussed the proposals with their Argentinian counterparts.

Pressed on whether the Argentinians could propose such a solution, he said: "When we sit down we will discuss everything that has to be discussed, not before. You don't discuss through the media. You discuss face to face. That is why I asked for a meeting with William Hague and he refused. If I can sit down with him, he will know what we think, but he refuses to sit down with us."

An exile during the military junta that invaded the islands leading to a total of 907 deaths, he ruled out any Argentinian intention to settle the dispute through force. He said: "I am a victim of a dictatorship, please take me more seriously. Argentina is a country which has not been in a war under a democratic government for over 100 years." He pointed out Britain had invaded Argentina three times in the past.

He denied the Argentinians had been making life difficult for the Falklands Islanders, instead accusing the British government of taking unilateral decisions including giving fishing licences for 25 years instead of, as in the past, just two years. He also accused Britain of exploring for oil in a way that could cause a real ecological disaster.

He said drily: "Wherever there is a smell of oil, big powers start to look around and they find a reason to stay there. I think probably oil will complicate the peaceful solution that is asked for by the United Nations. I think in history that Britain has had a tendency to stay in places where there are natural resources belonging to other people."

He also denied that his government was seeking to distract from its economic problems by highlighting the conflict. Taking a swipe at the state of the British economy, he said: "I think it is the United Kingdom that is going through an economic crisis and is becoming isolationist more than Argentina. They want to get out of the European Union, there is a sense here [in Britain] that we want to stop the world and get out."

He also said that at least under the Labour government Gordon Brown had been willing to meet the Argentinians.

The foreign minister ended with a plea for Hague to meet him, saying he was willing to stay in London for extra days until the foreign secretary could find a slot in his diary.

He said: "I hope that one day soon we can start a dialogue and not be hostage to a group of people who are there because a colonial empire took them and sent them there to settle and to live. There are other issues we should be discussing and hope we can discuss them."

A spokesman for the Foreign Office reiterated the foreign secretary's refusal to meet Timerman without Falklands Islands representatives present.

"We are still very much open to a meeting with Mr Timerman and the original appointment is still in the foreign secretary's diary for tomorrow. We hope that he will accept this offer and that we can engage in a meaningful discussion on issues of mutual interest. Mr Timerman's own plans in the UK are clearly focused on the Falkland Islands issue and since we remain concerned about the Argentine government's recent behaviour towards the Falkland Islanders, it is right and proper that their political representatives are involved in the part of the meeting that concerns them. We continue to make that clear to the Argentine government in diplomatic exchanges and the foreign secretary's offer of a meeting on these terms still stands."