The fighting took place in Lal Chowk, the main business centre at the heart of Srinagar, Kashmir's summer capital, and fighting was continuing, police said.
"One or two militants are believed to be hiding in a hotel in Lal Chowk and they are lobbing grenades and firing intermittently," a police officer told Reuters.
Kashmir is the core dispute between Pakistan and India and the cause of two of their three wars since their independence from British rule in 1947.
Separatist insurgents backed by Pakistan have been fighting Indian security forces in India's part of the Himalayan region for the past 20 years.
After a period of relative calm, militants have stepped up attacks across Kashmir, where officials say tens of thousands have been killed since 1989.
Last week four soldiers were killed when militants ambushed a security patrol in south Kashmir. (Reporting by Sheikh Mushtaq; Editing by Bappa Majumdar and Nick Macfie)
- Reuters - Thomson Reuters Foundation
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