Their chances of survival were bleak, officials said.
"We have again started the search operation this (Tuesday) morning to locate the missing people," Jaideep Singh, commanding officer, National Disaster Response Force (NDRF) told IANS.
Five bodies were fished out Monday and airlifted to Hyderabad.
Singh said a team of 84 people, comprising 10 underwater divers have started the search operation in the river from Thalaut near Hanogi Mata temple, the accident spot, to the Pandoh dam.
The dam is some 15 km downstream from the accident spot.
Official sources said a team from the Indian Army also started the search operation Tuesday.
More than 60 students and faculty members of the V.N.R. Vignana Jyothi Institute of Engineering and Technology in Hyderabad were on an excursion to Manali.
Some of them were getting themselves photographed on the bank of the river when the sudden rush of water washed them away.
The river level suddenly increased due to release of water from a nearby hydropower project's dam without warning, eye witnesses said.
The Himachal Pradesh High Court said it was not only a case of callousness but a grave negligence.
"It's a sad tale by reason of the fact that sheer fun of the young students turned out to be fatal as a consequence of utter and callous negligence of the power project authorities," Justice Tarlok Singh Chauhan said, taking suo moto notice of the incident.
He directed the state government to file a status report on the incident by June 16.
The accident spot is located some 200 km from state capital Shimla and on the border of Kullu and Mandi districts.