Unidentified gunmen barged into a villager's house in Mawar and opened fire, killing Sarwa Begum, 55, and her daughter, Farida Banu, 22, a police officer said on condition of anonymity.
Mawar is a remote village, 95km north of Srinagar, the summer capital of India's Jammu-Kashmir state.
In a separate pre-dawn raid on a house in Srinagar, paramilitary soldiers and police killed an alleged separatist fighter, police officer Javid Ahmad said.
Police identified the slain man as Bilal Ansari of Hizb al-Mujahidin, the largest Kashmiri separatist group. Ansari's brother, Muhammad Yusuf, was arrested during the raid, Ahmad said.
Hizb al-Mujahidin is one of more than a dozen groups fighting Indian security forces for Kashmir's independence or its merger with Pakistan.
Elsewhere, suspected separatists shot and killed two men early Saturday in Sallar, 75km south of Srinagar, police said.
Meanwhile, in Kangan, suspected separatists attacked an army patrol, killing a soldier and wounding another, police said. Kangan is about 45km northeast of Srinagar.
No other details were immediately available and there was no way of verifying the police claims.
The separatists have pledged to continue their attacks, despite the resumption of talks between India and Pakistan to resolve their differences over the Himalayan region, which both claim in its entirety.
Tens of thousands of people, mostly civilians, have been killed in the conflict since 1989.