Erdogan has refused to condemn Saudi Arabia's execution of prominent Shiite cleric and activist Sheikh Nimr al-Nimr this month. The execution sparked outrage in Shiite-majority areas of the Middle East, and protesters in Iran attacked two Saudi diplomatic missions, prompting Riyadh to sever diplomatic ties.
"We strongly condemn our president being directly targeted in certain articles in Iranian outlets controlled by the Iranian authorities... and demand that these articles cease immediately," the Turkish foreign ministry said in a statement.
It added that attacks on the Saudi embassy in Tehran and the kingdom's consulate in Iran's second city Mashhad were "unacceptable and deplorable".
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Turkey formally abolished the death penalty in 2004 as part of its bid to join the EU.
Erdogan on Wednesday said that Nimr's execution was an "internal legal matter" for Saudi Arabia, and ties between Ankara and Riyadh have improved in recent months. The Turkish leader visited Riyadh last month in a new sign of warming bilateral ties.
Turkey and Saudi Arabia, both overwhelmingly Sunni Muslim powers, share the same vision over the conflict in Syria where they believe only the ousting of President Bashar al-Assad can bring an end to almost five years of civil war.
Meanwhile, tensions have increased between Turkey and overwhelmingly Shiite Iran, which along with Russia is the key remaining ally of Assad.