The unknown assailant opened fire at Reina nightclub early on Sunday, before managing to flee amid the chaos.
The suspicion has fallen on the Islamic State group, linked to at least two terror attacks in Turkey last year.
President Recep Tayyip Erdogan said such groups tried "to create chaos".
The banned Kurdistan Workers' Party (PKK) has distanced themselves from the killings, with the PKK's Murat Karayilan quoted as saying they would "never target innocent civilians".
Earlier, Interior Minister Suleyman Soylu confirmed a "manhunt for the terrorist is under way. Police have launched operations. We hope the attacker will be captured soon."
According to the state run Anadolu Agency, over half of the victims in the seven minute attack were foreigners.
(Excerpts from BBC News)