Troops have been patrolling streets, erecting barricades and blocking roads leading to the UN offices.
Marches last week led to police killing at least 22 Muslim demonstrators, including a senior separatist leader, inflaming passions in one of the biggest separatist protests since a revolt against Indian rule broke out in 1989.
Unmogip, one of the oldest UN missions, monitors a 1949 ceasefire line dividing Kashmir between India and Pakistan.
Leaders of Kashmir's main separatist All Parties Hurriyat (Freedom) Conference alliance said they wanted to submit a memorandum to the UN office on Monday.
"Call upon India to end its forcible occupation of Jammu and Kashmir and desist from use of brute force against the people of Jammu and Kashmir," the memorandum, published in local newspapers, stated.
Protests have raised tensions between India and Pakistan who claim the region in full but rule in parts.
The crisis began after the state government promised to give forest land to a trust that runs Amarnath, a cave shrine visited by Hindu pilgrims. Many Muslims were enraged.
The government then rescinded its decision, which in turn angered Hindus in Jammu who attacked lorries carrying supplies to the Kashmir valley and often blocked the region's highway, the only surface link with the rest of India.
As a further consequnce, Kashmiri Muslims, challenging what they said was an economic blockade, took to the streets to protest.