The pilgrimage was flagged off in the morning at the Bhagwati Nagar base camp in Jammu by Nawang Rigzin Jora, Jammu Kashmir Minister for Tourism and Culture.
This batch along with about 2,500 pilgrims shall proceed for the holy cave shrine from Baltal base camp on Tuesday morning, Jun 16.
Located in Jammu Kashmir, the Amarnath caves are one of the most famous shrines in Hinduism and dedicated to the Lord Shiva.
The main shrine is claimed to be over 5,000 years old and forms an important part of ancient Hindu mythology.
Inside the main Amarnath cave lies an ice stalagmite, worshipped by devotees as the Shiva Lingam (the phallic symbol of Shiva), which waxes during May to August and gradually wanes thereafter.
This Lingam is said to develop and shrink with the phases of the moon, reaching its height during the summer festival.
According to Hindu mythology, this is the cave where Shiva explained the secret of life and eternity to his divine consort Parvati.
There are two other ice formations representing Parvati and Shiva's son, Ganesha.
The cave is situated at an altitude of 3,888 m (12,760 ft), about 141 km (88 mi) from Srinagar, the capital of Jammu and Kashmir.