"We have determined that Mehmet Ozturk, born in 1992 in Gaziantep, has carried out the heinous attack on Saturday in Istanbul", Mr Ala said.
Carnations and messages are left at Saturday's explosion site in Istanbul, where a suicide attack on the main pedestrian shopping street killed five people, including two dual nationality Israeli-Americans. An offshoot of the PKK claimed responsibility for both bombings.
According to the Jerusalem Post, Mr Netanyahu had ordered his foreign ministry to demand an official condemnation and apology from the Turkish government. "We are in close touch with Turkish authorities and reaffirm our commitment to work together with Turkey to confront the evil of terrorism".
Jens Stoltenberg, Secretary-General of North Atlantic Treaty Organisation (of which Turkey is a member), declared the attack was "yet another terrorist outrage targeting innocent civilians and our ally Turkey".
Another alleged IS member, Savas Yildiz, had been initially named by Turkish media as the suspected bomber.
Istanbul's governor says one person who was severely wounded in the suicide attack in the city has died, raising the death toll to five. Dogan reported that Ozturk's father and brother were among those held.
The third victim was identified Sunday as Avraham Goldman, 69, from Herzliya. "We also pray for the speediest recovery of the injured", it added.
The bodies of the three Israelis were to be flown home Sunday for burial aboard an Israeli military jet, Israeli military sources said. A foreign ministry spokeswoman said the decision would be made at short notice.
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One of the officials said the bomber had planned to hit a more crowded location but was deterred by the police presence.
The attack also came less than a week after a auto bomb in Ankara killed more than three dozen people; that bombing was claimed by Kurdish militants.
The only attack in Istanbul since the summer, also blamed on IS, targeted the tourist quarter of Sultanahmet.
President Recep Tayyip Erdogan also vowed to defeat groups trying to harm Turkey.
The PKK, or Kurdistan Worker's Party, seeks an independent state in Turkey, and has been in an armed struggle with the government for decades.
Prime Minister Ahmet Davutoglu said the blast was "inhumane" and would not stop Turkey, which has been targeted by Kurdish rebels and Islamic State of Iraq and the Levant (ISIL) in recent months, from fighting "centres of terrorism".
According to a CNNTürk reporter on the scene, the suicide attacker was on his way to the actual target when the bomb accidentally went off in front of a kebab restaurant.