Three policemen were also missing after a large mob attacked a police station, set it ablaze and used its weaponary to shoot and injure three cops, police said.
Amid the protests, militants attacked a police station in Pulwama, which was thwarted by the security forces.
In view of the volatile situation, Amarnath Yatra was also suspended, with police saying it will be resumed "as soon as it is possible to ensure security of yatris".
Union Home Minister Rajnath Singh also expressed "deep anguish" over the "loss of precious lives in the incidents of violence" in Kashmir and appealed for calm.
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As Burhan, the 21-year-old poster boy of Hizbul Mujahideen militant outfit, was laid to rest in his native place Tral, violent mobs attacked installations of police and paramilitary forces at various places in the Valley and set ablaze several buildings including three police installations, as a result of which three cops were missing.
"We have had a very difficult day today," said ADGP (CID) of J&K Police S M Sahai while describing the situation "bad in certain segments", "not critical" in areas like north Kashmir and under control in Srinagar.
Nine people were killed in the clashes between violent protestors and security forces at various places in the valley that erupted a day after Burhan's killing.
Eight were killed in "retaliatory" action by security forces, Sahai said, adding one person died due to drowning.
The militants are trying to "superimpose their attacks" on public protests, he said, while informing that there was also a militant attack on District Police Lines in Pulwama which the security forces thwarted.
To a volley of questions, including why Burhan was gunned down and not caught alive, Sahai said, "We certainly don't want to kill youngsters of our own society."
Mehbooba, while appealing for calm, said "violence only
She asked people, especially the youth "not to fall prey to the machinations of the vested interests, who play politics over the dead bodies of Kashmiris."
In a statement, the Chief Minister said, "I express profound grief over the tragic death of the youths and extend my heart-felt condolences to the bereaved family members in their hour of immense grief."
Mehbooba said disproportionate use of force for crowd control results in loss of precious lives and grave injuries which should be avoided at all costs.
She asked the police and the paramilitary forces to use Standard Operational Procedure (SOP) while dealing with protesters to avoid loss of precious human lives or injuries.
The protestors, who went on rampage in several areas, attacked police camps at Sangam, Larnoo, Seer, Gopalpora, Minority camp Mattan, Kokernag, Dooru and Janglat Mandi, police said.
"The funerals became an issue today and in the background of the funerals, there were several attempts at various locations particularly on security forces establishments, police stations, other government buildings houses of politicians, army camps. These were attacked at many isolated locations also which led to a very critical situation in which there have been eight casualties today," Sahai said.
The police officer said a mob attacked police station Damhal Hanjipora and it was burnt down, adding the weapons that were snatched from the police station were used to fire upon the police personnel.
"We did try to show restraint. They took 20 of our policemen hostage, three of them got bullet injuries while three of them are still missing," he said.
Sahai said 96 security forces personnel and around 30 civilians were injured in the clashes during the day.
The police official said the incidents of arson and stone-pelting took place on Achabal police station, in Kokernag, where a house of the MLA was burnt down, and Kund, Qazigund, on a minority camp in Vessu.
Violent incidents of arson and stone-pelting were also reported from Awantipora, Pulwama, Bomai, Sopore, Baramulla, Palhallan, Delina, Gantamullah, Sheeri, Kreeri, Lalpora, Bandipora, Narbal, Lasjan, Barzulla, Nowgam, Tengpora and Batamaloo. At many places, the mobs forcibly tried to enter the security force establishments.
In the BSF camp in Bandipora, a picket was set on fire, Sahai said, adding some of the security installations in CRPF camps were also set on fire.
Apart from that, there is report of about 96 security personnel and police personnel who have been injured in the attempt to tackle the situation, he said.