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 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 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.
In his first spoken comments on the attack, Erdogan said the aim was "to create a fissure and polarise society".
He insisted Turkey would resist efforts to divide the country, vowing 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.
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.
Almost forty Turkish soldiers have been killed in the operation and today, Dogan news agency reported one soldier was killed and four were injured in an IS attack in Al Bab.
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