Indian troops overnight shot and killed a separatist fighter after he infiltrated into the border district of Poonch from the Pakistani-zone of the divided state, police said.
"Other militants managed to flee back across the Line of Control (LoC)," a police spokesman said.
The infiltration was the first sighted by Indian troops since Home Minister Shivraj Patil last week said there had been a 60% decline in separatists incursions from Pakistan.
Nuclear-armed India and Pakistan hold Kashmir in parts and claim it in full. They have fought two of their three wars over the region.
Pakistan says it is doing its best to prevent separatists from crossing over to Indian Kashmir.
Police say suspected separatists hanged a civilian in Rajouri district and shot dead two more separatists when they opened fire at a shop in Anantnag district.
Protesters demand action against
Indian forces for some activities
Police also recovered the body of another person in northern Kupwara district overnight. "He had been abducted by militants two months ago," a spokesman said.
No group has claimed responsibility for the killings.
Meanwhile, several thousand villagers on Monday blocked Kashmir's main highway near Patan, 30km north of the summer capital Srinagar and held an anti-government demonstration, police and witnesses said.
They were demanding action against Indian security force personnel who had allegedly asked a Kashmiri man to dig out a landmine they suspected was buried near a busy road.
They said the man was critically injured as the mine exploded the moment he touched it with a shovel.
He was being treated in Srinagar's main hospital.
Muslim-majority Kashmir is in the grip of a 15-year-old insurgency that has left dead more than 40,000 people by official count. Separatists put the toll at between 80,000 and 100,000.