Turkish Interior Minister Abd al-Kadir Aksu said the attacks were the work of two bombers who detonated explosive-laden trucks outside the Neve Shalom and Beth Israel synagogues.
He vowed to catch all the culprits.
"We have footage from the security cameras of Neve Shalom. The truck exploded as it was driving past," Aksu told the Vatan newspaper, adding that one of the bombers was captured on film.
"He is in the footage, although it is not clear. We are trying to establish their identities... It is also not clear whether they were Turkish citizens or foreigners," he added.
The mass-circulation Sabah newspaper reported that police had established that one of the trucks used was registered to a man in the eastern city of Bingol.
The truck-owner's brother had been under surveillance for links to a radical Islamist Turkish group and had fought in the wars in Bosnia and Chechnya.
Prime Minister Recep Tayyip Erdogan, who was hosting a meeting of his cabinet on Monday, said Turkey was trying to confirm al-Qaida claim that it was responsible for the bombings.
"We have footage from the security cameras of Neve Shalom. The truck exploded as it was driving past"
Abd al-Kadir Aksu
Interior Minister, Turkey
Turkish officials have already said they believe a major foreign organisation was behind the blasts and have largely discounted an initial claim by a local underground Islamist group.
The Arabic-language statement from a branch of al-Qaida also warned of attacks by "cars of death" in the United States and its key allies including Britain, Australia and Japan.
"Abu Hafz al-Masri Brigades struck a mortal blow after having kept Jewish intelligence agents under surveillance and determined that five of them were in two synagogues in the centre of Istanbul," it said.
Justice Minister Cemil Cicek acknowledged on Sunday that the government might need to review its intelligence operations following reports that Israel had warned Ankara over possible al-Qaida attacks against Jewish targets, including the Neve Shalom synagogue.
London-based Arab newspaper Al-Quds Al-Arabi on Sunday said it received a claim of responsibility from al-Qaida for the explosions which ripped through two synagogues in the heart of historic Istanbul on Saturday, killing 23 people and injuring 300 more.
Six of the victims of the attacks were identified as Jews, one of them an eight-year-old girl, with most of the others Muslim passers-by and at least one policeman.
The bombings were the latest in a series of strikes against Jewish targets, including attacks in the Moroccan city of Casablanca in May that killed 45 and an attack on an Israeli-owned hotel in Kenya a year ago that left 18 dead.