The curfew was ordered in the major towns of the district to help prevent protests over the deaths of the civilians, the Hindustan Times reported.
Police erected barricades in the city of Srinagar to restrict the movement of vehicles.
Local officials and the Border Security Force reported different versions of what led to the alleged killings Thursday, the Hindustan Times said.
Local officials said protests erupted after the Border Security Force roughed up a religious leader's brother following an argument.
The Border Security Force dismissed that allegation and said a mob attacked its camp.
The force said up to 800 people attacked the post, fired at officials and attempted to storm a storehouse of arms.
"Keeping in view the threat to the arms and ammunitions, steps were taken with maximum restraint by the security forces," said Rajeev Krishna, a Border Security Force inspector general. "It is difficult to say in whose firing the casualties were caused."