The Turkish security forces were carrying out an operation in the town of Nusaybin in Mardin province where the government has been waging a blistering offensive against the outlawed Kurdistan Workers Party (PKK).
A senior police officer was hit by gunfire and later died, and four other members of the security forces, including a major in the gendarmerie and another senior police officer, died in two separate bomb attacks.
Hundreds of security forces have been killed in the region, while government says thousands of PKK militants have died.
Ankara launched the offensive against the PKK after the collapse in 2015 of a two-year long ceasefire with the group that has been a thorn in its side for three decades.
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The renewed conflict has also struck the heart of the country, with two attacks that killed dozens in the capital Ankara claimed by Kurdish rebels, at a time when citizens are already on high alert over bombings by the Islamic State group.
"These people don't deserve to be our citizens. We are not obliged to carry anyone engaged in the betrayal of their state and their people," he said.
A day after his comments his Justice Minister Bekir Bozdag said: "Of course we will begin work on this".