All the missing were undergoing training at a mountaineering institute but far from the avalanche site, Kumar said.
Uttarakhand state's top elected official, Pushkar Singh Dhami, said the National Disaster Response Force and the Indian army deployed teams to help with rescue efforts. The Indian air force deployed two helicopters to search for the missing.
"It has happened for the first time in the history of Indian mountaineering that such a large group of trainee mountaineers has been killed in an avalanche," said Amit Chowdhary, an official at the International Climbing and Mountaineering Federation and a former Indian air force officer.
Defence Minister Rajnath Singh said he was "deeply anguished" by the loss of lives in the avalanche.
"My condolences to the bereaved families who have lost their loved ones," Singh tweeted.
Avalanches are common in the mountainous areas of Uttarakhand. Last year, a glacier burst in the state, resulting in a flash flood that left more than 200 people dead.