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Syria's foreign ministry quickly responded by accusing Erdogan of himself supporting terrorist groups fighting Assad in Syria's civil war.
Turkey has demanded the removal of Assad from power and backed rebels fighting to overthrow him, but it has toned down its demands since it started working with Assad's allies Russia and Iran for a political resolution.
"Assad is definitely a terrorist who has carried out state terrorism," Erdogan told a televised news conference with his Tunisian counterpart Beji Caid Essebsi in Tunis.
"It is impossible to continue with Assad. How can we embrace the future with a Syrian president who has killed close to a million of his citizens?" he said, in some of his harshest comments for weeks.
Though Turkey has long demanded Assad's removal, it is now more focused in Syria on the threat from Islamist militants and Kurdish fighters it considers allies of the Kurdistan Workers' Party (known as the PKK), who it says have formed a "terror corridor" on its southern border.
Turkey says the Syrian Kurdish YPG militia, which Ankara views as an extension of the outlawed PKK which has fought an insurgency in southeast Turkey since the 1980s, cannot be invited to Syrian peace talks in the Kazakh capital Astana.
The YPG is the main element in a force that Washington has assisted with training, weapons, air support and help from ground advisers in the battle against Islamic State. That U.S. support has angered Ankara, a NATO ally of Washington.
Despite its differences with Russia and Iran, Turkey has worked with the two powers in the search for a political solution in Syria.
Ankara, Moscow and Tehran also brokered a deal to set up and monitor a "de-escalation zone" to reduce fighting between insurgents and Syrian government forces in Syria's rebel-held northwestern Idlib province.
"We can't say [Assad] will handle this. It is impossible for Turkey to accept this. Northern Syria has been handed over as a terror corridor. There is no peace in Syria and this peace won't come with Assad," Erdogan said.
Syria's state news agency SANA quoted a foreign ministry source as saying Erdogan "continues to misdirect Turkish public opinion with his usual froth in an attempt to absolve himself of the crimes which he has committed against the Syrian people through advancing support to the various terrorist groups in Syria."