The deceased, including two women, belonged to Uttar Pradesh, Bihar, Rajasthan, Assam, Haryana, and Madhya Pradesh, they said. Sixteen of the injured persons were critical, the officials added.
"The 17th batch of Amarnath yatra left from Bhagwati Nagar, Jammu, at 4:06 am today. At 1:45 pm, one of the SRTC buses met with a fatal accident and rolled down into a nallah near Nachilana Army camp in the jurisdiction of Banihal Police Station," a police spokesman said.
Theinjured pilgrims were rescued and the bodies were retrieved in an operation launched by the Army, the CPRF and police, with the help of locals of the area, he said.
As many as 20 injured pilgrims were airlifted to the Government Medical College (GMC) Hospital for treatment and eight were shifted to SKIMS hospital in Srinagar by ambulances, he said.
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Two of those with minor injuries were discharged. The bodies were airlifted to the GMC hospital, Jammu, for identification and for other legal and medical formalities.
Prime Minister Narendra Modi expressed pain at the loss of lives of in the accident and announced an ex-gratia of Rs 2 lakh for the next of kin of those killed and Rs 50,000 for the seriously injured.
"Extremely pained by the loss of lives of Amarnath Yatris due to a bus accident in J&K. My thoughts are with the families of the deceased," Modi tweeted.
The JKSRTC ordered an in-house inquiry into the road accident.
"An in-house inquiry committee has been constituted to look into the circumstances that led to this tragic accident involving an SRTC bus carrying the Amarnath yatris," its Managing Director Mir Afroz Ahmad said.
Defence Minister Arun Jaitley, Home Minister Rajnath Singh, J&K Chief Minister Mehbooba Mufti expressed condolences at the loss of lives.
Home Minister Singh spoke to Jammu and Kashmir Governor N N Vohra and Chief Minister Mufti and took stock of the situation, officials said.
Earlier, on July 10, militants attacked a bus carrying pilgrims in which eight persons lost their lives.
The CRPF acted as the first responder at the accident site today as a team deployed in Ramban immediately rushed to there along with doctors, ambulances and a Quick Action Team (QAT), a CRPF spokesman said.
"Once again the commitment of the CRPF was evident by their prompt action..The personnel of the force were also present at the Jammu airport from where the injured yatris were rushed to GMCH, Jammu," he said.