They say militants shot dead five Hindu civilians, including two women, in a village in the Rajouri district in Jammu.
In another incident, militants ambushed a police patrol vehicle in the Budgam district 30km east of the summer capital, Srinagar, killing three officers.
Police officers, firing back at their assailants, killed a militant.
Some reports say in a third attack on a remote village, gunmen shot dead three people including a soldier, although this has not been confirmed
This sudden escalation in militant violence comes just a week before voters in Indian-administered Kashmir go to polls for state legislative assembly elections.
Indiscriminate firing
A number of militant groups which have been fighting Indian authority in the region for over a decade, oppose the polls, and have threatened anyone who takes part in them.
Correspondents say militants have targeted Hindu civilians in several recent high-profile attacks in and around Jammu although Muslims too have been killed.
Last night's attack in the remote Doodasan Pain village in Rajouri was similar to an assault on a neighbouring village last month in which eight Muslims died.
Police officer SS Birjal told the Reuters news agency that on Sunday night, gunmen burst into the village, barged into Hindu households, and "they fired indiscriminately."
Mr Birjal said the victims had refused to move out of the area after last month's attack in the neighbourhood.
Contrary positions
State assembly elections, which begin in the Rajouri area on 16 September, are being staggered in four stages to ensure adequate security presence during polls.
Delhi says a peaceful atmosphere during the polls will be a test of Islamabad's pledges to stop infiltration of militants across the Line of Control (LoC) dividing the disputed region between the two neighbours.
Both countries have massed large forces along the LoC and along their borders since a militant attack on the Indian parliament last December.
Clashes between the two nuclear-armed armies, and between militants and Indian forces, have threatened to escalate out of control, eliciting repeated Western diplomatic initiatives to reduce tensions.
Islamabad has urged immediate peace talks while Delhi insists talks will only be held once "cross-border terrorism" is ended.
Despite stringent security measures, militant violence has seen an increase since polls were announced by Delhi.