Historians and opposition politicians have accused the Indian government of trying to privatize historical sites, including the world famous Taj Mahal.
The "Adopt a Heritage" plan aims to allow the upkeep and maintenance of 95 historic sites to be taken over by private firms.
India's tourism ministry has already announced a $3.7 million five-year contract with the Dalmia Bharat conglomerate to run Delhi's 17-century Taj Mahal, according to Agence France-Presse.
In exchange, Dalmia Bharat will be allowed to put up advertising, set ticket prices and earn money from sales.
The chief minister of West Bengal state, Mamata Banerjee, said Saturday that the "Red Fort" should not be "leased out," adding the decision was a "sad and dark day in our history."
Other monuments on the list include the 12th-century Unesco-listed Qutub Minar complex, also in Delhi.