The incident occurred at the hotel on an island in Srinagar's Dal Lake, a site popular with tourists and locals, sparking panic, an Indian police spokesman said on Tuesday.
The al-Mansurain group claimed responsibility, saying one of its squads had stormed the zone in the heart of the houseboat-dotted lake.
The privately-run Star News television network said an Indian soldier was killed and that three fighters were holed up on the lake's island.
The police spokesman was unable to confirm the report, but said there had been "intermittent firing" on the island.
Indian troops had rushed to the site of the fighting in patrol boats and cordoned off the area, police said.
Witnesses said the shooting caused panic among hundreds of foreign and domestic visitors staying in houseboats on the lake and around it.
"The sound of shots being fired definitely worried the tourists for some time," houseboat owner Abd al-Rashid said.
Elsewhere in Kashmir on Tuesday, rebels killed a worker in northern Baramulla district while Indian troops shot two alleged fighters in the same district and a third in Pulwama, 50km south of Srinagar.
Thousands of people have died in disputed Kashmir over the last 15 years.