Prime Minister Narendra Modi in a series of tweets appealed for peace ahead of the verdict, expected around 10:30 a.m. (0500 GMT). He had earlier cautioned his council of ministers from making unnecessary statements on the issue that could stoke public sentiments.
Appeals for peace have also come from Hindu and Muslim organizations and various political leaders. India's Home Ministry has asked all states to be on alert.
Authorities increased the security in Ayodhya, 550 kilometers (350 miles) east of New Delhi, and deployed more than 5,000 paramilitary forces to prevent any attacks by Hindu activists on Muslims, who comprise 6% of the town's more than 55,500 people.
Earlier, authorities banned the assembly of more than four people at one place in and around Ayodhya, a town in the northern state of Uttar Pradesh.
The Uttar Pradesh government ordered all the schools and colleges to remain closed until Monday.
The destruction of the mosque in 1992 sparked massive Hindu-Muslim violence that left 2,000 people dead.
Hindu hard-liners say they want to build a new temple to Hindu god Ram on the site, which they revere as his birthplace. They say the mosque was built after a temple dedicated to the Hindu god was destroyed by Muslim invaders.
After the demolition of the mosque, Hindus and Muslims took the issue to a lower court, which in 2010 ruled that the disputed land should be divided into three parts - two for Hindus and one for Muslims.
That was challenged in the Supreme Court by the two communities represented by Hindu Maha Sabha, the Sunni Waqf Board, and the Nirmohi Akhara.
The five judges started daily proceedings in August after mediation failed to find a compromise.
Modi had promised to build the temple in 2014 elections that brought him to power. But he later decided to wait for the court verdict despite pressure from millions of Hindu hard-liners who asked his government to bring legislation to build the temple.