A top official said curfew has been imposed across the Valley and restrictions put in place to avert fresh trouble.
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.
Chief Minister Mehbooba Mufti appealed for calm while expressing "profound" grief and agony over the deaths during the protests and asked security forces to avoid use of disproportionate force for crowd control.
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Burhan's funeral was attended by thousands of people. There was no deployment of security forces in Tral and adjoining areas to avoid a confrontation with the people coming to participate in the funeral.
"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.
Eight were killed in "retaliatory" action by security forces, Sahai said, adding one person died due to drowning.
"It is very unfortunate that young lives were lost in clashes," Sahai told reporters and appealed to the parents to restrain their children from participating in such protests so that young lives are not lost.
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.
He said the Hizb commander and two others got killed when security forces retaliated after being fired upon by the trio from a house in which they were hiding. Two security personnel were injured in that firing, he added.