One Turkish soldier was killed in the fighting.
The government has imposed 24-hour curfews in the towns of Cizre and Silopi, allowing troops and police backed by tanks and armored vehicles to battle militants linked to the Kurdistan Workers' Party, or PKK, who have moved their fight for autonomy to some towns and city neighborhoods.
The government says the militants have placed explosive devices, dug trenches and set up barricades in Cizre and Silopi and has vowed to press ahead with the operations until no armed rebel remains in the two towns.
A military statement today said 56 Kurdish militants were killed in Cizre and six died in fighting in Silopi since Tuesday. The soldier was killed in a battle in Cizre.
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At least eight security force members were wounded, the state-run Anadolu Agency reported.
Turkey's pro-Kurdish People's Democracy Party says at least 63 civilians have been killed by security forces' operations during curfews that have been enforced in 17 locations since August.
The European human rights body, the Council of Europe, has expressed concern over the curfews that bar residents from leaving homes and prevent observers or journalists from monitoring conditions. Turkey says the curfews aim to prevent civilian deaths.