Wajid Khan says 22 troops were also wounded in Thursday’s gunbattle in the northwestern Kurram tribal region.
He says the fighting began when a group of Pakistani militants attacked a security post. The troops returned fire and killed 20 militants.
The death toll could not be independently confirmed as the fighting was in a remote mountainous area that is off-limits to journalists.
Kurram is considered a main base for the Pakistani Taliban.
Scores of insurgents are believed to be hiding there after escaping military operations in the nearby tribal regions in recent years.