The statement by the extremist group -- which Turkey is fighting in neighbouring Syria -- was the first undisputed claim it has made for an attack in Turkey despite being blamed for several assaults over the last year.
Anti-terror police made their first arrests over the attack, which unleashed scenes of panic among party-goers at one of Istanbul's swankiest venues and killed mostly foreign tourists.
The shooting took place just 75 minutes into 2017 after a bloody year in Turkey in which hundreds of people were killed in violence blamed on both IS jihadists and Kurdish militants.
In a statement circulated on social media, the jihadist group said one of the "soldiers of the caliphate" had carried out the attack on the Reina nightclub.
It accused Turkey, a majority-Muslim country, of being a servant of Christians, in a possible reference to Ankara's alliance with the international coalition fighting IS in neighbouring Syria and Iraq.
People place flowers and candles at a police barrier in front of the Reina night club (AAP) Source: AAP
'Continue with determination'
The IS statement said the attack was in response to Turkey's military intervention against the jihadists in war-ravaged Syria where Turkish troops are pressing on with a four-month incursion to oust IS jihadists the border area.
Turkey is also spearheading a ceasefire plan with Russia to form a basis for peace talks on Syria.
But after a cabinet meeting in Ankara chaired by President Recep Tayyip Erdogan, the government vowed that the operation in Syria, dubbed Euphrates Shield, would continue.
"This was a message for our cross-border operations, above all the Euphrates Shield," said Deputy Prime Minister Numan Kurtulmus.
"We will carry on our cross-border operations and Euphrates Shield and with determination," he added.
After a lightning successful start to the operation recapturing towns from IS including Jarabulus, the Turkish military has taken dozens of casualties as it tries to capture Al Bab where IS has put up a stronger fight to remain in control.
Hurriyet daily said investigators believe the gunman may be from the Central Asian states of Kyrgyzstan or Uzbekistan.
The attacker may be linked to the same cell that in June carried out a triple suicide bombing and gun attack at Istanbul's Ataturk airport blamed on IS that left 47 people dead, the paper added.
But pro-government daily Yeni Akit caused a furore on social media with a headline declaring the United States was the "number one suspect" over the attack.
- 'Panicking and blood' -
Twelve Turks were killed in the attack alongside 27 foreigners, including one Belgian-Turkish dual national. Sixty-five people were wounded.
The foreigners who died -- most of them from Arab countries and including Muslims -- had come to the club to celebrate a special night in style.
They included three Lebanese nationals, two Jordanians and three Iraqis, officials in their respective countries said. At least one German was killed.
A Canadian woman, a Russian woman and a teenage Arab Israeli were also among the dead. Turkish press reports said at least seven Saudi nationals died but this has yet to be confirmed by Riyadh.
Indian film producer Abis Rizvi, son of a former MP, was also among those killed, prompting tributes from the Bollywood community.
The attack evoked memories of the November 2015 carnage in Paris when IS jihadists unleashed a gun and bombing rampage on nightspots in the French capital, killing 130 people including 90 at the Bataclan concert hall.
"I think back to those moments, I can't erase them from my memory," survivor Yusuf Kodat from Alsace in France told AFP as he returned to the scene of the attack by the Bosphorus.
"The people panicking, the blood, the noise of the gunshots, the explosions. That's what I keep on thinking about," Kodat said.
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Australians warned be cautious in Istanbul
Australians visiting Istanbul have been warned to avoid the nightclub district as the manhunt continues for a gunman who opened fire on New Year revellers.
In what is believed to be a terrorist attack, the gunman dressed in a Santa Claus costume shot his way into the Reina nightclub.
At least 39 people, including many foreigners, were killed and 69 were wounded.
The Department of Foreign Affairs and Trade on Monday updated its travel advice for Turkey.
"Avoid the area, exercise heightened caution and remain vigilant to your personal safety and surroundings," the Smart Traveller website says.
It advises people to reconsider the need to travel to Ankara and Istanbul.
Acting opposition leader Chris Bowen condemned the "barbarous" attack and expressed sympathy for the victims and their families.
DFAT has not received any reports of Australians being caught up in the attack.
