Yasin Malik was arrested for defying the curfew
Muslims in Indian-administered Kashmir have defied a curfew imposed ahead of a rally that had been planned in the region's largest city, Srinagar.
At least four people were killed in confrontations with police. Earlier, three prominent separatist leaders were placed under arrest.
There have been massive rallies in recent weeks in support of independence from India.
Both India and Pakistan claim sovereignty over Kashmir.
The strength of the protests is an embarrassment for the Indian authorities, the BBC's Altaf Hussain in Srinagar says.
Despite large numbers of police and paramilitary troops on the streets there were demonstrations in many places in defiance of the curfew which was imposed early on Sunday in many areas of the region.
India's Central Reserve Police Force (CRPF) opened fire killing one person after hundreds of people tried to march from Narbal, eight kilometres (five miles) from Srinagar to the location of Monday's planned rally, the Lal Chowk (Red Square) in the city.
A second person was killed in Pulwama, south of Srinagar, another died in the northern area of Handwara and a fourth person was killed in Hajin, a village nearly 30 km (20 miles) from Srinagar.
In another attempt to dampen the protests, separatist leaders Syed Ali Shah Geelani and Mirwaiz Omar Farooq were arrested at their homes on Sunday night.
Separatist leader Yasin Malik was arrested on Monday when he tried to defy the curfew by leading a procession of some 30 people.
On Sunday one person was killed and another wounded as police fired on a crowd in Srinagar.
Thousands of troops are enforcing the curfew in Srinagar
The valley is already paralysed by a strike called by separatist groups who want an end to Indian rule, with shops, banks and schools shut.
Thousands of troops have been drafted in to patrol Srinagar's streets.
Local media say 15 journalists were among those beaten by police on Sunday as they tried to cover the protests, despite having curfew passes.
The strikers want a referendum which they hope will lead to self-determination for the region.
On Friday, hundreds of thousands of Muslims took part in a protest rally called by separatist leaders in Srinagar.
Speaking before his arrest, Mr Farooq said the Indian authorities were afraid of "peaceful but massive demonstrations for freedom".
"Such repressive measures will not work. We will emerge stronger and more vibrant," he told the AFP news agency.
The strike comes amid continuing separatist violence in the region.
Fifteen people died in a gun battle on Friday between militants and the authorities near the Line of Control - the de facto border dividing Kashmir between India and Pakistan.
Army officials said three soldiers were critically wounded during the battle, which they said was the fiercest this year in Kashmir.
The recent trouble started when the state government said it would grant 99 acres (40 hectares) of forest land to a Hindu trust, the Amarnath Shrine Board.
Muslims launched violent protests, saying the allocation of land was aimed at altering the demographic balance in the area.
The government said the board needed the land to erect huts and toilets for visiting pilgrims.
But following days of protests, the government rescinded the order, prompting Hindu groups to mount violent protests of their own.
Those protests continued on Monday with around 40 people, including 10 policemen injured. The city of Jammu and neighbouring areas was shut down again. Hundreds of Hindu protesters took to the streets and police used tear gas to disperse them.
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