ISTANBUL—Kurdish rebels killed at least 14 policemen and Turkish special-operations battalions crossed into northern Iraq in pursuit of rebel forces, as the long-running conflict between Turkey and its Kurdish insurgency escalated.

The policemen were killed in two separate rebel attacks Tuesday in eastern Turkey, official media said, on the same day Prime Minister Ahmet Davutoglu attended funerals of 16 soldiers killed by a roadside bomb on Sunday.

With...