NEW DELHI—Indian security forces hunted suspected militants at an air force base near the country’s border with Pakistan after two days of running gun battles that left at least seven Indian security personnel dead, posing a challenge to recent efforts at reconciliation between the estranged neighbors.

The government said four attackers were killed Saturday. There was a shootout with two others Sunday, authorities said. There was no immediate claim of responsibility. A senior Indian Home Ministry official, who declined to...