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Was IS behind this? Analysis by Mark Lowen, BBC News, Istanbul
IS is known to have operatives in Gaziantep.
Turkey has been hit by a series of bombs both by IS and Kurdish militants in the past year. The last IS attack, on Istanbul airport in June, killed more than 40 people.
The jihadists have recently lost ground in northern Syria, including a former stronghold, Manbij. Syrian rebel soldiers are preparing to advance further into the IS-held province of Jarablus.
If this bomb was the work of IS, there will be speculation it was a revenge attack, intended as a show of strength by a group on the defensive.
In a written statement published by local media (in Turkish), Mr Erdogan argued there was "no difference" between IS, the Kurdish militants of the PKK, and followers of US-based cleric Fethullah Gulen, whom he blames for the coup attempt last month.
"Our country and our nation have again only one message to those who attack us - you will not succeed!" he said.