The Indian army said four militants were shot dead in a clash in the state’s Kupwara district on Sunday.
Another three rebels were killed after they tried to storm a government office in Poonch district.
A curfew has been in effect for over two months across Kashmir following an upsurge of violence since 9 July.
The protests were sparked by the killing of a popular militant leader. Burhan Wani, 22, died in a gunfight with the Indian army.
More than 70 people, mostly young men, have since been killed in clashes between protestors and security forces, and thousands more injured in the worst violence seen in the region for years.
On Sunday Indian soldiers killed four militants as they tried to cross the de-facto border that divides the disputed Himalayan region between India and Pakistan in Kupwara, an army official said.
“They tried to infiltrate into Nowgam sector (an area northwest of the main city of Srinagar) and were intercepted. Four militants were killed and their AK rifles were recovered,” army spokesman NN Joshi told the AFP news agency.
Three other rebels were killed after they tried to enter a government office in Poonch. A policeman was also killed in the clash.
The clashes with militants came as stone-pelting residents protesting against Indian rule of the region clashed with security forces in Pulwana and two other places in the southern Kashmir valley, leaving many injured, police said.
Disputed Kashmir is claimed in its entirety by both India and Pakistan and has been a flashpoint for more than 60 years, sparking two wars between the countries.
Within the disputed Muslim-majority territory, some militant groups have taken up arms to fight for independence from Indian rule or a merger with Pakistan.