Interior Minister Suleyman Soylu told reporters that 20 victims have been identified.
"15 of the victims are foreigners while the other five are Turkish citizens," the minister said, adding that efforts continue to identify the other bodies.
Soylu stated security forces were hunting down the terrorist, saying, "Our law enforcement has launched an operation. We hope he or she will be caught before long."
Health Minister Recep Akdag told reporters, after he and Soylu visited some of the wounded people at a hospital, that 65 people were in several hospitals, receiving treatment.
"Four of those injured are in a critical condition," Akdag said, adding that a large number of foreign nationals were also injured.
Turkish Family and Social Policies Minister Fatma Betul Sayan Kaya said there were Saudi Arabian, Moroccan, Lebanese, Libyan nationals among the attack victims, along with several other foreign nationals.
"Many of those foreign nationals came to Turkey numerous times. They know about Turkey. We have victims who are Turkish nationals as well but many of those victims were foreign nationals," she said.
Foreign Minister Mevlut Cavusoglu shared a message via his Twitter account, and said "terrorism aims to attack our unity."
Earlier, Governor Vasip Sahin described the attack in Ortakoy, Besiktas, as “cruel” and an “act of terror”.
“At 1.15 a.m., a terrorist carrying a long-barreled weapon martyred the police officer waiting outside, and then martyred another citizen to enter” the club, he said.
“The terrorist then carried out this violent and cruel act by spraying bullets on innocent people who were celebrating the new year," Sahin said.
An investigation is underway and the governor’s office would provide further updates, he added.
Meanwhile, a security meeting took place in Istanbul's Dolmabahce Palace following the terror attack. The meeting was chaired by Prime Minister Binali Yildirim, started at 1 p.m. local time (1000GMT) and lasted almost two hours.
Deputy Prime Minister Numan Kurtulmus and several ministers also attended the meeting.
President Recep Tayyip Erdogan issued a message after the terror attack and said Turkey would fight against terrorism and its backers "till the end".
Turkish General Staff has issued a written statement from its official website as well, condemning the attack and offering condolences to the victims' families and wishing a speedy recovery for the injured.
"Our fight against terrorism will continue with same dedication and effort," it said.
The attack happened three weeks after twin bombings in Istanbul killed at least 45 people, most of whom were police officers.