The assailant stormed the glamorous Reina nightclub on the Bosphorus early on Sunday morning, spraying 120 bullets at terrified partygoers celebrating the start of 2017.
Of the 39 dead, 27 were foreigners including citizens from Lebanon, Saudi Arabia, Israel, Jordan, Iraq, Tunisia and Morocco.
At least 36 people have now been detained in the probe, but the gunman himself remains on the run after slipping into the night following the attack.
“The identity of the person responsible for the attack has been established,” Foreign Minister Mevlut Cavusoglu said during an interview with state-run Anadolu news agency, without giving any name.
The attack was claimed by the Islamic State (IS) jihadist group, with reports suggesting the authorities suspect the gunman may be from either Kyrgyzstan or Uzbekistan, both ex-Soviet states.
“Efforts to capture him continue,” said Cavusoglu, adding that the house the suspect lived in “has been searched” and that the attack he mounted had been “professionally” planned.
IS took responsibility for the massacre in a statement on Monday, marking the first time it has issued a clear and undisputed claim for a major attack inside Turkey.
Hitting a nightclub on New Year’s night, the attack struck at the heart of secular Turkey, with analysts saying IS clearly sought to widen splits in Turkish society.
In his first spoken comments on the attack, Erdogan said the attack’s aim was “to create a fissure and polarise society”.
He insisted Turkey would resist efforts to divide the country, vowing that Turks would “stand tall and keep our sangfroid. “
“No-one’s lifestyle in Turkey is under a systematic threat. We would never let this happen. In 14 years in power, we have never given this a chance,” Erdogan said in a speech at the presidential palace in Ankara.
IS said the attack was a response to Turkey’s military intervention against the jihadists in war-ravaged Syria where Turkish troops are pressing a four-month incursion to oust jihadists from the border area.
Since the lightning advance into northern Syria in August, removing IS elements from the Turkish border, Ankara has faced a tougher fight to capture the town of Al Bab from IS.
But Erdogan insisted the operation would continue and Turkey would clear areas wherever “terrorist organisations” are.
“The operation in Syria’s Al Bab will be finished in a short time, God willing,” he said.
In the western city of Izmir, at least 20 people including 11 women were taken into custody as part of the investigation into the attack, Anadolu reported.
The news agency said they were of Central Asian and Syrian origin while Dogan news agency said they were members of three families.
It was alleged that some of those detained had been living in the house with the suspected attacker in Konya.
The new arrests bring the number of those detained to at least 36, including two foreigners detained by Turkish police at Istanbul’s main airport on Tuesday.
One of them was reportedly a woman suspected of being his wife with whom he had stayed in Konya along with two children.
Dogan news agency quoted her as saying she was not aware of the attack until it was reported.
On Wednesday, the Haberturk daily said that during his getaway, the gunman took a taxi to a Uighur restaurant in the city’s Zeytinburnu district where he got out and went inside to get money from someone to pay the fare.
The restaurant owner told the paper that police had since detained seven of his workers — all of them Turkic Uighurs from the Xinjiang region of China — but that he did not know the attacker himself.
The shooting occurred after a bloody year in Turkey in which hundreds of people were killed in violence blamed on both IS jihadists and Kurdish militants.
Turkey is also still reeling from a failed July 15 coup blamed by the government on the US-based Islamic preacher Fethullah Gulen that has been followed by a relentless purge of his alleged supporters from state institutions.
Parliament on Tuesday extended a controversial state of emergency in place since the coup — and which has seen over 41,000 people arrested — by another three months to April 19.