There have been many anti-India demonstrations in Srinagar
An indefinite curfew is being strictly enforced in Indian-administered Kashmir to prevent a rally against Indian rule by the separatist groups.
Groups demanding an end to Indian rule had urged their supporters to rally on Monday in Lal Chowk, the square in the heart of Srinagar city.
Security forces are out in force in the Muslim-majority Kashmir valley.
The leaders of the political separatist group, the All Party Hurriyat Conference, are under detention.
They include Yasin Malik who was arrested on Sunday and Syed Ali Shah Geelani and Mirwaiz Umar Farooq who have been put under house arrest.
The BBC's Altaf Hussain in Srinagar says that police are even reported to be patrolling small villages in the Kashmir valley where they do not usually go.
One protest was reported in the town of Baramullah - but it was against the Pakistani President Asif Zardari who was quoted in the Wall Street Journal as describing militants in Kashmir fighting against India as "terrorists".
On Sunday police vans mounted with loudspeakers drove through the streets before dawn, telling people to stay inside, and thousands of soldiers were deployed in Srinagar and other large towns.
"The Lal Chowk rally should be symbolic and every individual should try to join to convey to the world the Kashmiris' resolve for the right to self-determination," Syed Ali Shah Geelani said before his house arrest.
The authorities, however, made clear that the demonstration would not be tolerated.
"Please co-operate," Kashmir's senior official, Anil Goswami, said on television. "If you violate the curfew, security forces will respond."
After years of relative calm in the Kashmir Valley, recent months have seen some of the most intense anti-India feeling for about 20 years.
The tensions over the summer were sparked by a plan to grant land to a board that oversees the running of an important Hindu shrine.
The proposal led to serious friction between the Muslims of the valley and their neighbours in the Hindu-dominated Jammu region.
The dispute fuelled anti-India sentiment in the valley, and there was a series of large marches.
More than 30 people have been killed by the police since the protests began in August.
The authorities have been criticised by Amnesty International and other human rights organisations for allowing the use of lethal force against unarmed protestors.
The demonstrations subsided during the Muslim holy month of Ramadan, but now that it has ended the separatist groups had been hoping to re-ignite them with Monday's proposed rally.