The libertarian is less hostile to Britain than his Left-wing predecessor Alberto Fernandez, who demanded immediate negotiations to end what he called an “anachronistic colonial situation” on the islands.
Argentina has claimed the Falklands since its independence in the 19th century and failed to seize them by force during the 1982 Falklands War.
Mr Milei lauded Margaret Thatcher, who is still reviled in Argentina for ordering the sinking of the General Belgrano cruiser, as one of “the great leaders in the history of humanity” during his campaign.
The remark drew condemnation from war veterans and his main presidential rival, Sergio Massa.
But Mr Milei stuck to his guns in an attempt to distance himself from the confrontational approach of his predecessor and to ingratiate himself with the West, whom he has said he will look to for international support.
Mr Milei has nevertheless asserted Argentina’s “non-negotiable” sovereignty over the Falklands, which Argentina refers to as the Malvinas Islands.
“We had a war – that we lost – and now we have to make every effort to recover the islands through diplomatic channels,” he said in the final televised election debate.
His position is that any transfer of power should be peaceful and that Argentina first needs to transform its economy, where inflation is running rampant at 143 per cent.
Diana Mondino, a close adviser of Mr Milei who it has been suggested may become his foreign minister, said in September that the population of the Falklands – 99.8 per cent of whom voted to remain British in a 2013 referendum – “cannot be disrespected”.
“The concept that one can impose on people what can be done or what should be done, it’s so feudal and naive,” she said.
Ms Mondino added that Argentina needed to “become a normal country” to persuade Islanders to seek closer ties.
“How would anyone not born and bred in Argentina understand [our] inflation?” she said. “Why would anyone want to become a part of a society – we need to become a normal country, and we’re an empty country,” she said.
‘‘It may take many years but you cannot force on other people any decisions. Not on Argentinians, not on anyone. You cannot force decisions anymore, that has to stop.”
A gradual transfer of power
In a country where the Falklands remain an intensely sensitive political issue, Ms Mondino’s remarks had sparked speculation that she could be sacked.
But Mr Milei has stood by her and has strongly advocated a gradual transfer of power, suggesting Hong Kong as a model to imitate.
“Britain had a similar situation with China over Hong Kong, and through diplomacy a solution was reached and the English returned the enclave,” he said in September.
“In such a process we can’t leave out those people who live in the Islands, we must include the interests of people living in the Islands.”
The Falklands are located in the South Atlantic about 370 miles from the Argentine mainland.
Argentina claims it possesses “legitimate and inalienable sovereignty” over the islands and the corresponding maritime waters.
A statement on the Argentine government’s website said: “The recovery of these territories and the full exercise of its sovereignty, respecting the way of life of its inhabitants and following the principles of International Law, constitutes a permanent and irrevocable objective of the Argentine people.”