Islamic State has claimed responsibility for the attack, saying it was revenge for Turkish military involvement in Syria.
Turkish media reports have said the attacker is believed to be an ethnic Uighur, possibly from Kyrgyzstan.
The shooting in Istanbul's Ortakoy neighbourhood, an upscale district on the Bosphorus shore, came after a year in which NATO member Turkey was shaken by a series of attacks by radical Islamist and Kurdish militants and by a failed coup.
President Tayyip Erdogan said the attack, which targeted a club popular with local celebrities and moneyed foreigners, was being exploited to try to divide the largely Sunni Muslim nation and that the state never meddled in how people lived.
"There is no point trying to blame the Ortakoy attack on differences in lifestyles," he said in a speech to local administrators at the presidential palace in Ankara.
"Nobody's lifestyle is under systematic threat in Turkey. We will never allow this," he said in comments broadcast live. It was his first public speech since the shooting.
Turkey's Religious Affairs Directorate, which condemned the attack in its immediate aftermath, had issued a statement in December saying celebrating the New Year did not fit with Muslim values, triggering criticism from some parts of Turkish society.
Such calls have made many secular Turks suspicious of the Islamist background of Erdogan and the ruling AK Party, seeing them as bent on eroding the secular principles of the modern republic founded in 1923 by Mustafa Kemal Ataturk after the fall of the Ottoman empire. Erdogan rejects such suggestions.