The IS-linked Aamaq News Agency said the attack was carried by a "heroic soldier of the caliphate who attacked the most famous nightclub where Christians were celebrating their pagan feast."
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It said the man opened fire from an automatic rifle in "revenge for God's religion and in response to the orders" of IS leader Abu Bakr al-Baghdadi.
The group described Turkey as "the servant of the cross."
Earlier, Turkish media reports had said that Turkish authorities believed the IS group was behind the attack and that the gunman, who is still at large, comes from a Central Asian nation and is likely to be either from Uzbekistan or Kyrgyzstan.
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According to Hurriyet and Karar newspapers, police had also established similarities with the high-casualty suicide bomb and gun attack at Istanbul's Ataturk Airport in June and was investigating whether the same IS cell could have carried out both attacks.
The gunman killed a policeman and another man outside the Reina club in the early hours of 2017 before entering and firing at an estimated 600 people partying inside with an automatic rifle.
Nearly two-thirds of the dead in the upscale club, which is frequented by local celebrities, were foreigners, Turkey's Anadolu Agency said. Many of them hailed from the Middle East.
The mass shooting followed more than 30 violent acts over the past year in Turkey, which is a member of the NATO alliance and a partner in the U.S.-led coalition fighting against the Islamic State group in Syria and Iraq. The country endured multiple bombings in 2016, including three in Istanbul alone that authorities blamed on IS, a failed coup attempt in July and renewed conflict with Kurdish rebels in the southeast.
The Islamic State group claims to have cells in the country. Analysts think it was behind suicide bombings last January and March that targeted tourists on Istanbul's iconic Istiklal Street as well as the attack at Ataturk Airport in June, which killed 45 people.
In December, IS released a video purportedly showing the killing of two Turkish soldiers and urged its supporters to "conquer" Istanbul. Turkey's jets regularly bomb the group in the northern Syrian town of Al-Bab. Turkish authorities have not confirmed the authenticity of the video.
Prime Minister Binali Yildirim said the attacker left a gun at the club and escaped by "taking advantage of the chaos" that ensued. Some customers reportedly jumped into the waters of the Bosporus to escape the attack.
Bassem Mroue reported from Beirut. Suzan Fraser in Ankara, and Cinar Kiper in Istanbul, contributed to this report. null