"We consider it to be a terrorist act as a result of an attacker, whom we consider to be a woman, detonating the bomb," Oktay told reporters Sunday.
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CCTV footage shows a woman sitting on a bench for more than 40 minutes and then getting up one or two minutes before the explosion, leaving a bag or plastic bag behind, according to Turkish Justice Minister Bekir Bozdag.
Bozdag, who made the comments in an interview with privately owned A Haber news channel, said Turkish security forces believe the woman is the suspect, and officials are investigating her.
"There are two possibilities. Either that bag or plastic bag has a mechanism in it, it explodes on its own or someone detonates it from afar. All of these are currently under investigation." he added.
"The name of the woman is unknown," he said. "All the recordings and data about the woman are being analyzed."
The blast happened on Istiklal Street in Beyoglu Square, in the heart of Turkey's largest city, Istanbul Governor Ali Yerlikaya said.
"We wish God's mercy on those who lost their lives and a speedy recovery to the injured," Yerlikaya tweeted.
The six people killed include Yusuf Meydan, a member of Turkey's Ministry of Family and Social Services, and his daughter Ecrin, according to Derya Yank, the minister of the agency.
Turkey's Health Minister Fahrettin Koca tweeted Sunday evening that 39 of the 81 people injured in the explosion have been discharged from the hospital after completing their treatment.
"Of the 42 patients that remain hospitalized, five are still in the intensive care unit, two of them are in serious condition. We are doing our best to ensure that the injured people recover as soon as possible," Koca said.
'What looked like the aftermath of a war zone'
Witness Tariq Keblaoui said he was shopping on Istiklal Street when the explosion happened about 10 meters (32.8 feet) ahead of him.
"People were scattering immediately," said Keblaoui, a Lebanese-based journalist who was on his last day of vacation in the city.
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"Very shortly after, I could see how many injured were on the ground," Keblaoui told CNN. He says he saw dead bodies and victims who were seriously injured.
"There was a man in the store bleeding from his ears and his legs, and his friends were crying near him," Keblaoui said.
Istiklal Street was packed with visitors when the blast happened Sunday afternoon, he said.
"It went very quickly from a very peaceful Sunday with a very crowded street full of tourists to being what looked like the aftermath of a war zone," Keblaoui said.
'There is a smell of terror'
Earlier Sunday, Turkish President Recep Tayyip Erdogan said the explosion might be terror-related, but he was not yet certain.
"It may be wrong if we say this is definitely terror, but according to preliminary findings, what my governors told us, that there is a smell of terror here," Erdogan said at a news conference.
He said authorities were reviewing CCTV footage.
"All the responsible figures will be identified and punished," the president said.
Erdogan said he and his delegation would continue plans to attend the G20 summit in Bali, Indonesia.
Istanbul's Chief Public Prosecutor's Office has launched an investigation, the country's official Anadolu news agency reported. At least eight prosecutors have been assigned, the vice president told reporters.
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The city's criminal court issued a broadcast ban on all visual and audio news, as well on social media sites, related to the explosion, Anadolu added.
Countries unite in condemning the attack
News of the explosion led to a torrent of condolences from around the world.
French President Emmanuel Macron, whose own country suffered a deadly terror attack exactly seven years earlier, shared his sympathies for the Turkish people.
"On this day so symbolic for our Nation, while we think of the victims who fell on November 13, 2015, the Turkish people are struck by an attack in their heart, Istanbul," Macron tweeted Sunday. "To the Turks: we share your pain. We stand with you in the fight against terrorism."
European Council President Charles Michel shared his condolences after Sunday's deadly blast.
"Horrific news from Istanbul tonight," he said. "All our thoughts are with those currently responding and the people of Türkiye at this very distressing time."
NATO Secretary General Jens Stoltenberg tweeted his "deepest condolences" to the Turkish people, adding that NATO "stands in solidarity with our ally" Turkey.
The United States "strongly condemns the act of violence that took place today in Istanbul," White House Press Secretary Karine Jean-Pierre said Sunday. "Our thoughts are with those who were injured and our deepest condolences go to those who lost loved ones."
Ukrainian President Volodymyr Zelensky tweeted of his "deep sadness" at the news of the blast. "I offer my condolences to the families of those who lost their lives and wish a speedy recovery to the injured," Zelensky said. "The pain of the friendly Turkish people is our pain."
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