The pilgrims, comprising 1,638 males, 663 females and 180 sages, left for the base-camps in 66 vehicles, a police officer said.
The pilgrims are being escorted by Central Reserve Police Force (CRPF) vehicles, the officer said.
Meanwhile, another police official said, "The yatra began early this morning from both the routes. So far more than 500 pilgrims have paid obeisance at the cave shrine housing the naturally formed ice-lingam."
The pilgrimage had yesterday began from here with the first batch of 2,280 devotees leaving for the high altitude shrine.
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An ITBP officer had yesterday died of cardiac arrest near the cave shrine in South Kashmir, while a community kitchen operator died today after getting hit on the head by a rock at Brarimarg on Baltal route to the cave shrine.
The annual yatra began amid a terror threat which has prompted the authorities to mobilise the "highest level" of security measures including satellite tracking system.
"Intelligence input received from the SSP Anantnag reveals that terrorists have been directed to eliminate 100 to 150 pilgrims and about 100 police officers and personnel," according to a letter sent by IG (Kashmir zone) Muneer Khan to the Army, the CRPF, and range DIGs in the state on Sunday.
At this stage, the possibility of a sensational attack by a terrorist outfit cannot be ruled out, he said.
This year, the Amarnath yatra will be eight days shorter than last year's 48 days and will conclude on Shravan Purnima (Raksha Bandhan) on August 7.
Situated in a narrow gorge at the farther end of Lidder Valley, the shrine stands at 3,888 metres, 46 km from Pahalgam and 14 km from Baltal.