The clash occurred in Pulwama, where more than 40 Indian paramilitary police were killed in a bombing last week.
That attack, the worst in decades, has fuelled tensions between nuclear-armed India and Pakistan.
A civilian and three alleged militants were also among those killed in Monday's confrontation.
Police say the three suspected militants who were killed are members of Pakistan-based group Jaish-e-Mohammad (JeM), which said it was responsible for Thursday's suicide bombing.
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