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Efken Ala named the man as Mehmet Ozturk. He told reporters that five people had been questioned so far. 

Mr Ala announced a review of security measures in seven Turkish provinces following several attacks since July.

Meanwhile a soccer game between Galatasaray and Fenerbahce on Sunday night has been postponed.

A statement from the Istanbul governor's office said that the decision had been taken for security reasons "after the evaluation of credible intelligence".

Fans had already begun to arrive for the match at Galatasaray's Turk Telecom Arena when the announcement was made, leaving them with no choice but to leave the ground.

The postponement came even though the authorities have repeatedly urged the 15 million inhabitants of Turkey's largest city to carry on with their normal daily lives after the blast.

Three Israelis - two with Israeli-US nationality - and an Iranian died in the attack. Another 36 were injured. 

Eleven Israelis were among the injured. Two Irish citizens, one national each from Germany, Iceland, Dubai and Iran were also injured. 

The coffins of the Israeli nationals were being flown out on Sunday. The Israeli government advised its citizens to avoid Turkey.

"We have determined that Mehmet Ozturk, born in 1992 in Gaziantep, carried out the heinous attack on Saturday in Istanbul," Mr Ala told a news conference in the capital Ankara 

"It has been established that he is a member of Daesh," he said using another name for IS.

Turkey is part of the US-led coalition against IS and allows coalition planes to use its air base at Incirlik for raids on Iraq and Syria.

It has been attacked by IS in the past - most recently in January when a suspected suicide attack in Istanbul killed 12 German tourists.

And more than 100 people died outside Ankara railway station in October 2015 when IS militants carried out a double bombing close to the headquarters of the national intelligence organisation.

Kurdish militants have claimed a number of recent attacks in Turkey.

President Recep Tayyip Erdogan has said terror groups are targeting civilians because they are losing their struggle against Turkish security forces.