The second batch of 2,481 pilgrims, comprising 1,638 males, 663 females and 180 sages, left from Jammu in 66 vehicles for the twin base camps of the yatra.
A police officer said the pilgrims are being escorted by Central Reserve Police Force (CRPF) personnel.
"The pilgrimage began early this morning under overcast conditions from the twin routes of Pahalgam and Baltal.
"As many as 6,097 pilgrims performed 'darshan' of the naturally formed ice-lingam at the 3,880 metre high holy cave shrine on the first day," an official spokesman said.
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Intermittent rains lashed wide parts of Kashmir including the yatra route since yesterday, resulting in considerable drop in day and night temperatures.
Jammu and Kashmir Governor N N Vohra, who is also the chairman of the Shri Amarnathji Shrine Board (SASB) - which manages the affairs of the yatra - was among the first to reach the cave shrine.
He paid obeisance at the sanctum sanctorum of the shrine and participated in the 'Pratham Pooja' ceremony. Vohra prayed for sustained peace, harmony, progress and prosperity in the state, the spokesman said.
The governor stressed on the need for effective supervision and round-the-clock monitoring of the yatra management by the camp directors and all the functionaries concerned for ensuring smooth conduct of the pilgrimage.
While 4,853 pilgrims preferred Pahalgam route, 6,435 pilgrims left for the cave shrine from the Baltal route, the spokesman said.
A pilgrim, Bhushan Kotwal, a resident of Afgana Mohalla in Jammu, was injured by a shooting stone while he was on way to the shrine, between Railpathri and Brarimarg, along Baltal route at 6.20 am, the spokesman said.
Expressing grief over the death of the man, Vohra directed the chief executive officer of SASB, Umang Narula, to provide immediate relief of Rs three lakh to the next of the kin of the deceased.
He told the CEO not to wait for the processing of the insurance cover which the Board has provided for all pilgrims and service providers in case of accidental deaths.
The body has been handed over to his family for last rites after completion of formalities, a police official said.
The spokesman said adequate security arrangements have been put in place to ensure that the pilgrimage passes off peacefully.
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.
The government has mobilised a heavy security blanket of over 35,000 to 40,000 personnel including of the police, the Army, the BSF and the CRPF.
Meanwhile, the board has again appealed to the people to embark on the pilgrimage only after getting medically checked and obtaining a permit.
"This would ensure against any avoidable inconvenience to them," Narula said, adding the board has issued a detailed advisory of do's and don'ts to the pilgrims which has to be strictly adhered to.