Mr Milei, a right-wing libertarian economist, was elected as president of Argentina on Sunday night, defeating current economics minister Sergio Massa.
The new president said in a presidential debate that Argentina should have control of the islands, which it calls Las Malvinas.
The Falklands are a British overseas territory, which Argentina invaded in 1982, sparking a military response from the UK. More than 900 people died in the ensuing war, which resulted in the islands remaining under British control.
The population of the Falklands, which are 300 miles off the coast of Argentina in the south Atlantic, voted overwhelmingly to remain British in a 2013 referendum.
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