Separatists have called for a protest shutdown on Monday to commemorate the death of Hizbul commander Burhan Wani.
Wani was killed in Kokernag area of Anantnag district on July 8, 2016 in a gunfight with the security forces.
"No yatri convoy moved from Bhagwati Nagar Yatra Niwas in Jammu towards Kashmir Valley on Monday," a police officer said.
To date, 95,923 pilgrims have performed the Amarnath Yatra since it started on July 1. The 45-day long yatra will end on August 15, coinciding with the Shravan Purnima festival.
Situated at 3,888 metres above the sea-level in Kashmir's Himalayas, the Amarnath cave shrine houses an ice stalagmite structure that symbolises mythical p owers of Lord Shiva, according to the devotees.
The ice stalagmite structure waxes and wanes with the phases of the moon.
Jammu and Kashmir Governor Satya Pal Malik on Sunday said the annual Hindu pilgrimage has been possible with the support and assistance of the local Muslims.
Malik also asked people to bear with the curbs imposed on civilian traffic on the national highway for two hours daily as it concerns the safety and the security of the pilgrims.
"You know what happened on the national highway on February 14 this year," Malik said while he referred to the terror strike on the CRPF convoy in Pulwama district in which 40 troopers were killed.
Meanwhile, All India Radio (AIR) is starting an FM radio station in the Baltal base camp to flash weather forecasts, traffic information and devotion al content for the information of the pilgrims.
( With inputs from IANS )