Mohamed Hussain Shareef, an aide, said Nasir died at a hospital in Singapore after a long illness.
Nasir, whose ancestors had been sultans in the island country, served as prime minister in the last days of the British protectorate. He served as president from 1968 to 1978, the first president of the second republic.
After resigning from office, he spent the last decades of his life in Singapore.
The Maldives, in the Indian Ocean, include almost 1,200 small islands, 250 of them inhabited, split among 26 atolls. With about 300,000 residents, it is the smallest country in Asia in both population and area.
Nasir was credited with bringing the country in touch with the rest of the world, including attracting tourists, Miadhu News said. During his presidency, he introduced British-style education and radio and television and built the country's first international airport.
He also led the modernization of the country's fishing industry.