The Turkish official was one of three people shot dead last Wednesday when a gunman opened fire in a restaurant in the Iraqi Kurdish regional capital, Erbil.
The suspect in the assassination of the diplomat is the brother of a female member of the Turkish parliament, according to reports.
A statement from a Iraqi Kurdish security force, the Counter Terrorism Department, gave the suspect's name as Mazlum Dag.
Turkey's pro-Kurdish People's Democratic Party (HDP) later confirmed that the man who had been arrested was the brother of one of its lawmakers, Dersim Dag.
“Kurdistan will never become the headquarters of terrorism…criminals will never be able to hide,” Barzani, also the former president of the Kurdistan Region, said in a statement.
“I commend the security and anti-terror forces of the Kurdistan Region for arresting the suspects,” he said, calling for all parties to not bring their disputes to the northern region of Iraq.
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