Between 600 and 700 people are said to have been in the venue at the time of the attack.
The nightclub was packed with hundreds of people, and the BBCreported that some of the revelers jumped into the Bosphorus river to escape.
Turkish politician Suleyman Soylu told reporters following the attack: "A manhunt for the terrorist is under way".
Dogan reported that some witnesses claimed the assailants were "speaking Arabic" while NTV said special force police officers were still searching the club.
A terrorist opened fire on a famous Istanbulnightclub Saturday, marking the fourth major Turkish terror attack in less than a month.
"Fifteen of the victims are foreigners while the other five are Turkish citizens", the minister said, adding that efforts were continuing to identify the other victims.
The NYPD Counterterrorism Bureau said via Twitter that with regard to the Istanbul shooting, there were no specific threats to New York City. Russia's ambassador to Turkey, Andrey Karlov, was shot in Ankara on December 19 in an assassination apparently linked to Syria's civil war.
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Policemen secure the area after a gun attack on Reina, a popular night club in Istanbul.
Her husband's condition was not said to be serious.
"They say 35 to 40 died but it's probably more because when I was walking, people were walking on top of people", said Mr Boydas, who plays for Istanbul club Beylerbeyi SK.
White House official Ned Price said the attack on "innocent revellers" celebrating New Year's shows the attackers' savagery.
It is believed that the gunman carried out the attack alone, and that he left the club wearing different clothing to that he had on when he entered.
This year, President Recep Tayyip Erdoğan's Islamist government had told mosques around the country to declare New Year's Eve celebrations to be un-Islamic.
The hashtag #hükümetistifa (#GovernmentResignation) was used almost 7,000 times in the wake of the attack to protest the government and what many deem as a mismanagement of Turkey's national security. President Obama offered his condolences over the attack while on holiday in Hawaii.
The attack comes less than two weeks after the Russian ambassador to Turkey, Andrey Karlov, was assassinated while giving a speech at an art gallery in the capital Ankara.