"What the co-leader has done is treason, provocation," Erdogan told reporters at Istanbul airport before leaving for Saudi Arabia.
Selahattin Demirtas, co-leader of the pro-Kurdish Peoples' Democratic Party (HDP) said at the weekend that Kurds in Turkey had to decide whether to live in autonomy or "under one man's tyranny".
Erdogan condemned the comment as unconstitutional.
"How dare you talk about establishing a state in the southeast and in the east within Turkey's existing unitary structure," Erdogan said, referring to Demirtas.
Demirtas has emerged as Erdogan's key rival over the last year, with many commentators saying he is the only politician to rival the rhetorical skills of the president.
Turkish prosecutors yesterday opened a criminal investigation against Demirtas on accusations of committing crimes against the constitutional order.
Erdogan said: "I believe that the treachery network dealing a blow to our country's unity will learn a lesson it deserves from our people and from the law.
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