Police officers, many of them local Muslims, have been increasingly targeted in recent months in the territory rocked for decades by violence.
The abduction of 10 family members was carried out in three districts of southern Kashmir in retaliation for police arrests of the militants' relatives.
Sons, brothers and fathers of police officials have been abducted since Wednesday in three districts, including Kulgam, where five such abductions were carried out.
Dialogue is the only way forward for ties between Pakistan and India, the foreign minister in Islamabad said on Monday.
At least seven militants and a soldier were killed in gun battles in India-administered Kashmir, police said Saturday.
Government forces shot dead one protester and injured more than 120 others in Indian-administered Kashmir on Tuesday, just days after three civilians were killed in similar demonstrations in the restive region.
Army operations were halted on May 16 at the start of the fasting month.
Police in India's Kashmir investigating the killing of a prominent journalist and two of his security guards arrested a suspect on Friday, an official said.
Shujaat Bukhari, a leading journalist and editor of the English-language daily Rising Kashmir, was shot dead in Srinagar on Thursday.
Shujaat Bukhari, editor of the local daily Rising Kashmir, was shot at close range by unidentified motorcycle-riding gunmen.
Pakistan and India have promised to end ceasefire violations in disputed Kashmir, their militaries said, following the highest levels of violence between the rivals in the restive region in 15 years.