The one-day strike was called by the pro-independence Jammu and Kashmir Liberation Front (JKLF) in memory of founder Mohammad Maqbool Bhat, who was hanged in a New Delhi jail on February 11, 1984 for the murder of an intelligence officer. Supporters say the charges were trumped up.
The strike, also supported by other separatist groups opposed to Indian rule over part of the disputed Himalayan region, closed down most of the shops, businesses and offices in the region's summer capital Srinagar.
Traffic was also minimal.
Police used batons to beat back dozens of JKLF activists as they tried to reach a UN observer office in Srinagar to submit a petition asking for the UN's help in obtaining the return of Maqbool Bhat's remains.
Bhat was buried at New Delhi's Tihar jail.
The small UN office in Srinagar monitors the heavily militarised Line of Control dividing the disputed region into India and Pakistan-held Kashmir.
"The remains should be handed over to us for decent burial," said JKLF vice chairman Bashir Butt as police hauled him and dozens of his supporters into waiting trucks.
The JKLF launched an armed separatist insurgency against Indian troops in 1989, and the unrest has left more than 42,000 people dead by official count.
The group gave up its armed struggle in 1994, and is now campaigning for Kashmir's independence from both India and Pakistan, which hold the region in part but claim it in full.
Meanwhile, Indian troops shot dead five militants, three of them senior commanders, since Sunday evening, the army said.
"The dead include Hizbul Mujahedin's financial chief," army spokesman Colonel Manjinder Singh said, referring to region's most powerful rebel group.