In a second attack on Sunday, a police official escorting a group of civilians was killed when suspected rebels tossed a grenade at them in the Sarjankotal region of Doda district.
A civilian also died, while another was injured, the police source said.
Indian police sources put the overnight and Sunday toll at 13, but the Kashmir Media Service claimed that a further ten Kashmiris were killed in so-called “fake encounters”, where security services claim their civilian victims are "militants" after the event.
Eight were killed in the Kupwara district and two more in the Baramulla district, KMS said.
Unknown gunmen shot dead a Muslim, Bagh Hussain, in the village of Lower Saim in Rajouri district overnight, while his brother-in-law was abducted by the same group and his throat was slit on Sunday.
In the same district another Muslim was killed when he was caught in the crossfire between Indian troops and Muslim rebels.
Police said two more civilians were shot dead by unknown assailants, one of them a Sikh, Jang Bahadur Singh, in the districts of Anantnag and Baramulla late on Saturday evening.
The fresh killings brings to at least 184 the number of people who have died in Kashmir in an explosion of violence since 30 August
A Muslim man was killed and two of his relatives injured when they stepped over an abandoned explosive device in the village of Munwan in northern Kuwpara district overnight, police said.
Four more people, including a policeman and a rebel, were killed elsewhere in Kashmir overnight and on Sunday, police said.
Explosion of violence
The fresh killings brings to at least 190 the number of people who have died in Kashmir in an explosion of violence since Indian troops shot dead top rebel commander Gazi Baba in Srinagar on 30 August.
Baba, a Pakistani, had been on the list of most-wanted rebels after India accused him of masterminding an attack on its parliament in December 2001 that killed 15 people, including the five attackers, and triggered a military stand-off with Pakistan.
More than 38,000 people have died in Indian Kashmir since the launch of an anti-Indian insurgency in the region in 1989 by Muslim guerrillas. The separatists put the toll between 80,000 and 100,000.