The decision comes amid a top court hearing on an appeal against a 2010 lower court verdict that gave Muslims one-third of the land and the rest to Hindu groups.
The move comes as Prime Minister Narendra Modi's ruling alliance faces a tightening race for an election due by May.
Hindu groups believe the site to be the birthplace of Lord Ram, one of the religion's most revered deities.
Over 200,000 people are expected near the site where a Hindu mob in 1992 pulled down a 16th-century mosque, sparking deadly religious riots.
As millions of Hindus believe that the mosque stood at the birthplace of Lord Ram the dispute continues to be at the core of tensions between Hindus and India's Muslim minority.
Many Hindus believe the Babri Mosque was only built after the destruction of a temple on the same spot that marks the birthplace of their god Ram, and the issue remains hugely divisive.