Demonstrators tore down barbed wire barricades that authorities had erected on roads leading to the UN offices and chanted "Down with India."
Thousands of police and paramilitary forces in riot gear guarded the streets, but no violence was reported.
The weeks of unrest, which has left at least 34 people dead, have reinvigorated the region's decades-long separatist struggle, threatening to sever the ties between India and its only Muslim-majority state. They have also unleashed tensions between Kashmir's Muslims and Hindu minority, sparking fears that the troubles could spread to the rest of India, which has a history of religious violence.
While the latest unrest has been led by Kashmir's peaceful separatist groups, thousands of protesters yesterday chanted the name of Lashkar-e-Tayyaba, one of the most violent Islamic militant groups fighting to wrest the predominantly Muslim region from Hindu-majority India.
"Lashkar has arrived. It is your death, India. Lashkar has come," the crowd chanted as they passed Indian security forces.
Apart from its activities in Kashmir, the Pakistan-based group also has been blamed for deadly terror bombings across India in recent years.
Yesterday, activists delivered a petition to the UN offices in Srinagar, citing human rights violations by Indian authorities and requesting UN intervention, said Nazir Ahmed Ronga, a leading lawyer in the city.
Syed Ali Shah Geelani, a prominent leader, told the crowd to demand "the UN, the US, Britain, and international community to come and see what people want here."
"This is a struggle for right to self-determination," he said. "The UN should send its peacekeepers to Jammu as well as Kashmir." Jammu is the region's only Hindu-majority city.
Such talk is bound to irk Indian officials, who see the problems in Kashmir as an internal matter. India's Foreign Ministry last week tartly dismissed statements from Pakistan encouraging the protests.
The crisis caught Indian authorities off guard when it began in June with a dispute over land near a Hindu shrine. Muslims held protests complaining that a state government plan to transfer 99 acres to a Hindu trust to build facilities for pilgrims near the shrine was actually a settlement plan meant to alter the religious balance in the region.
A subsequent decision by the state government to scrap the plan angered the region's Hindus.