India's Supreme Court ruled on Nov. 9 that a 2.77 acre (1.1 hectare) plot of land should be awarded to Hindus, who believe it is the birthplace of Lord Ram, a physical incarnation of the Hindu god Vishnu.
"There are apparent errors in the Supreme Court judgment, and we felt that it would be prudent to file a review petition," Syed Qasim Ilyas, a member of the group, told a press briefing.
The main Muslim litigant in the case, the Sunni Wakf Board, has declined to file a review, saying it respected the verdict.
The site, where in 1528 a mosque was built by an associate of the Mughal emperor Babar, has been the centre of a bitter dispute between India's majority Hindus and Muslims, who make up about 14% of the population, since Indian independence.
In 1992, a Hindu mob razed the mosque to the ground, leading to riots in several parts of India.