A diplomatic offensive against Britain's oil exploration off the Falkland Islands intensified today as Argentina prepared to stake its case to the head of the UN backed by regional allies including Brazil.

The Argentinian president, Cristina Kirchner, said a summit of 32 countries in Mexico had endorsed a document accusing Britain of flouting international law by permitting drilling to begin this week.

The Rio Group summit made no immediate official statement, but Venezuela's Hugo Chávez and Nicaragua's Daniel Ortega demanded the UK hand back the Falklands to Buenos Aires.

The Argentinian foreign minister, Jorge Taiana, is due to meet the UN secretary-general, Ban Ki-moon, in New York today. The UN has called for talks between Britain and Argentina but has little power to intervene without the backing of the security council, where the UK can veto substantive resolutions.

The sovereignty standoff flared this month over the arrival of a rig, the Ocean Guardian, which is to drill offshore for oil and gas deposits. Last night, Brazil's president, Luiz Inácio Lula da Silva, criticised the UN for not pushing more forcefully to reopen the debate over the islands, which Argentinians call Las Malvinas.

"What is the geographic, the political or economic explanation for the UK to be in Las Malvinas?" he asked. "Could it be because the UK is a permanent member of the UN's security council where they can do everything and the others nothing?"

Today's Times newspaper said a resolution was set to be tabled in the UN general assembly condemning Britain for allowing the owner of the British rig, Desire Petroleum, to begin drilling 60 miles north of the islands after Argentina announced new shipping controls.

The defence minister, Bill Rammell, said the government would take "whatever steps are necessary" to protect the islands, which had a "legitimate right" to develop an oil industry within their waters.

At the Rio Group summit, Argentina presented a statement quoting the Mexican president, Felipe Calderón, as saying that "the heads of state represented here reaffirm their support for the legitimate rights of the republic of Argentina in the sovereignty dispute with Great Britain".

Kirchner ruled out any plans to try to keep the British boats or rigs out. "We do not believe in methods like blockades," she told reporters. But in her speech at the summit she reiterated Argentina's claim to the islands and blamed the Foreign Office for fanning tensions.

"When in these last few days England decided to install an oil rig offshore and Argentina – in exercise of its domestic law – made decisions as a sovereign state, the Foreign Office floated the idea of a potential war threat by Argentina.

"I would say that is ridiculous, cynical, because few countries have shown more signs of peaceful intentions than Argentina after the advent of democracy," she said according to an English translation of her speech posted on the presidency's website.

Jan Cheek, a member of the Falklands legislative assembly, said she was "not surprised" by the Latin American countries' statement, as they had historically tended to back Argentina in the dispute.

She said on BBC Radio 4's Today programme: "Argentina does regularly take this issue to the UN but it has very little effect on us, mainly because what they are seeking is to make us a colony of Argentina while we have freely chosen, through self-determination, to be an overseas territory of the UK."

Analysts said Buenos Aires scored a diplomatic victory in mustering regional solidarity but that the practical effects were negligible.