The bloc — made up of Brazil, Russia, India, China and South Africa — in August announced it was admitting six new members in a bid to counter the Western-led global order.
The membership of Argentina, Ethiopia, Iran, Saudi Arabia, Egypt and the United Arab Emirates was due to take effect from January 1, 2024.
The letters signed by Milei and published by several media houses said Argentina's membership was "not considered appropriate at this time."
The libertarian outsider Milei took office this month after his resounding defeat of Argentina's traditional political parties, and he had vowed on the campaign trail not to join BRICS.
In his letters he said his foreign policy "differs in many aspects from that of the previous government. In this sense, some decisions made by the previous administration will be reviewed."
During his election campaign, Milei said "our geopolitical alignment is with the United States and Israel. We are not going to ally with communists."
Despite vowing to cut ties with major trading partners China and Brazil, he has taken a more conciliatory tone since coming to office.
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