Two Indian air force helicopters were searching the mountains, but officials said the operation had to be suspended due to unfavourable conditions.
The missing group, including four Britons, two Americans, an Australian and an Indian, began climbing Nanda Devi on 13 May.
The British group leader's family said they were "deeply saddened".
Earlier, officials said four other British climbers had been rescued. They have been named by India TV as Mark Thomas, Ian Wade, Kate Armstrong and Zachary Quain.
They were airlifted to safety after being spotted early on Sunday at a base camp near Nanda Devi.
The four rescued mountaineers began their ascent with the eight-member group on 13 May but returned to Munsiyari base camp due to harsh weather conditions.
The larger group headed for the summit of another unnamed peak, government official Vijay Kumar Jogdanda said.
oth groups remained in touch until 26 May - a day before an avalanche hit the 7,816-metre mountain, according to authorities.
The missing group was being led by experienced British mountain guide Martin Moran, whose Scotland-based company Moran Mountain has run numerous expeditions in the Indian Himalayas.
In a statement, his family said they were pressing for the search area to be widened, and wanted it to continue until they had firm evidence of the "wellbeing or otherwise of all those in the climbing group".
Mountaineer Alan Hinkes told the BBC his friend, Mr Moran, is a "massively experienced mountaineer", adding: "There's still hope."
But he warned the monsoon season was now moving into the area, bringing with it heavy rain and fresh amounts of snow in the mountains.
"We are worried there's an avalanche involved and no matter how experienced you are, the mountain doesn't know that," he added.