The gondola lift at Gulmarg claims to be the world's highest, ferrying passengers to a height of 4,100m for panoramic views of the snow-clad Himalayas.
He said that a rescue operation was quickly started for about 100 other people who were stranded in other 15 cable cars.
The accident was the first since the cable cars were installed 18 years ago, Mr Hussain said.
Shah said among the seven dead includes four members of Andraskar family from Delhi. The three local residents who died included two tourist guides.
In a tragic incident, five tourists were killed when a tree fell on a ropeway in Jammu and Kashmir's Gulmarg.
All members of the family, along with three others, identified as Mukhtar Ahmed Ganie, Javed Ahmed Khandey and Farooq Ahmed and believed to be tourist guides, when their cable auto crashed in the Gulmarg resort following strong winds. The cable auto carries tourists in the Pirpanjal mountain range in the western Himalayas.
Former Jammu and Kashmir chief minister Omar Abdullah questioned why the cable vehicle service had not been shut down as a precautionary measure because of high winds.
The two-stage Gulmarg cable auto lift ferries people to a height of 13,780 ft above the sea level.
"What awful news", he tweeted.
Former Jammu and Kashmir chief minister Omar Abdullah questioned why the cable vehicle service had not been shut down as a precautionary measure because of high winds. "That's a laid down SOP".