He was speaking in a national address amid renewed tensions over the British overseas territory after US President Donald Trump hinted the US would not help the UK in a future conflict over the islands.
"I want to be quite clear with everybody. The Falklands are Argentinian. Historically and legally," Milei said.
"There can be no argument. They are part of the Argentine territory.
"The islanders on their usurped territory do not have a legitimate right to self-determination and any argument on any such self-determination is invalid."
He said the UK was facing "multiple crises on multiple fronts" and said he would sign decrees to introduce sanctions against any companies working on oil production in area.
Milei declared the Sea Lion oilfield, owned by an Israeli and a British firm where production is expected to begin in 2028, a "clear and present danger" to the country's claims.
"If we do not act swiftly in a few months, they will have the material capacity to access the oil that lies underneath our sea. Something that has never happened before," he said.
Announcing plans for a naval base in Tierre del Fuego in the south of Argentina, he said Trump and the US was "assessing their historical position in regard to the Falklands".
"That is not empty words as they understand that Argentina is a reliable partner and a valuable ally for decades to come," he said
"Our role and relevance as a country in the world has changed dramatically.
"The Falklands are our future - we need to recover these islands which are nationally relevant. There is no other path forward."
The US president suggested he would not back the UK in a fight over the territory.
Asked in an interview if he would "come to the aid" of the UK, the US president told GB News: "Well look, I was there when they had the first war.
"That was a long time ago and I watched it so carefully, and you comported yourselves very well.
"You took it back pretty strongly, but it's a long way away. That's a big trip, it's a long way.
"So, your country's not doing well. Don't forget, you get a big percentage of your oil from the Strait of Hormuz, and you weren't there to help me.
"Your country was not there to help me. We didn't need help, but I did ask NATO, and I asked your former leader, 'why didn't you send a couple of ships?'
"He said we don't have any, and it was pretty sad, the whole thing.
Downing Street said earlier this week the UK's position on the Falklands was "long-standing and unwavering".
"Sovereignty rests with the UK, and the islanders' right to self-determination is paramount.
"The UK's position is clear. The islanders have repeatedly expressed their wish to remain a British overseas territory."
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