ISTANBUL — More than 49 Kurdish insurgents were killed in the first two days of a new Turkish military offensive against P.K.K. rebels in southeastern Turkey and northern Iraq, the military said Saturday.

The military began the operation, involving heavy air support and more than 10,000 troops, on Thursday, a day after an attack by the P.K.K., or Kurdish Worker’s Party, killed 24 soldiers and injured 18 in the province of Hakkari, in one of the deadliest single-day attacks in recent years.

Part of the operation has extended into the autonomous Kurdistan region of northern Iraq, a mountainous border area where P.K.K. militants often take shelter. Turkey has staged cross-border operations or bombardment several times in recent years, and it is a thorny issue in Turkey’s relationship with Iraq.

“Operations that are conducted in several locations across the border and two locations in the country, and aim to prevent separatist terror organization actions against our units in the country and along borders, continue,” the military’s statement said. No predicted end date for the operation was given.