One person was killed in firing by security forces on a mob in Kupwara district of Kashmir, police sources said.
There were some other incidents of violence, including a militant strike on a police post and a mob attack on the family of a police officer in which his wife and daughter were injured.
In Delhi, Modi held a high-level meeting to review the Kashmir situation soon after his return from his five-day Africa visit. It was attended by Home Minister Rajnath Singh, Finance Minister Arun Jaitley, Defence Minister Manohar Parrikar, External Affairs Minister Sushma Swaraj and National Security Adviser Ajit Doval.
"He (PM) has appealed to the people of Jammu and Kashmir to maintain peace so that the situation can normalise. He (PM) also expressed hope that no innocent person should face any kind of inconvenience or loss," Minister of State in the Prime Minister's Office Jitendra Singh said after the meeting.
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Modi said the Centre will provide whatever help is needed by the state government, according to Jitendra Singh.
The Prime Minister was given a detailed presentation of the situation prevailing in the Valley.
"The Prime Minister kept taking updates about the Jammu and Kashmir situation during his visit abroad. The biggest evidence of his concern is that he called this review meeting within hours of returning from the tour and took details," Singh told reporters.
In Kashmir, while normal life remained paralysed, unidentified militants targeted a police post in Sopore, about 55 kms from Srinagar, firing seven to eight rounds but no one was injured.
In Awantipora area of Pulwama in south Kashmir, a mob beat up and injured wife and daughter of a police Sub- Inspector Mohammad Ashraf Pal and damaged his house.
The injured were shifted to Sub District Hospital Awantipora where their condition is stated to be stable.
Meanwhile, restrictions continued on the movement of
people in Srinagar and four districts of south Kashmir, officials said.
The strike called by the separatist groups also affected normal life in the Valley.
Shops, private offices, business establishments and petrol pumps remained shut, while government offices and banks witnessed thin attendance, the officials said.
Public transport was completely off the roads for the fourth consecutive day, while private cars and auto-rickshaws were seen plying at few places in the areas where there were no restrictions, they said.
Educational institutions in the Valley were closed on account of the ongoing summer vacations, while Central University of Kashmir (CUK), Kashmir University, Islamic University of Science and Technology (IUST) and Jammu and Kashmir Board of School Education (JKBOSE) have postponed the examinations due to the prevailing situation.
The strike was then extended for two more days to protest the killings of civilians in firing allegedly by security forces.
The shutdown call was again extended yesterday.
Most of the separatist leaders, including Syed Ali Shah Geelani, Mirwaiz Umer Farooq and Mohammad Yasin Malik, are either in custody or house arrest.