UPDATE 1:22 p.m. EST:
An American man survived the Istanbul shooting by playing dead, USA Today reports. Jacob Raak said he was visiting friends for his 35th birthday when he was shot in the leg.
"I just let him shoot me," he said. His brother said he avoided serious injury because the bullet hit his phone.
Meanwhile, the U.S. Embassy in Ankara insisted it had no knowledge of a threat to the club, despite rumors on social media insisting otherwise.
ISIS's Aamaq News Agency said the shooter had taken orders from leader Abu Bakr al-Baghdadi.
The shooter is believed to be from Uzbekistan or Kyrgyzstan, according to Turkish media reports.
Hundreds of people were inside the Reina nightclub when the shooter attacked just after midnight on Sunday. Officials said the gunman was believed to have been wearing a Santa Claus costume.
Of the 39 people killed, all but one have been identified as of early Monday morning, officials said.
Several WNBA players were next door to the nightclub at the time of the shooting. They were playing in a Turkish basketball league in the offseason, and all were unhurt.
Turkey has partnered with the anti-ISIS coalition in Syria in Iraq. ISIS has responded with repeated attacks in Turkey.
The Associated Press contributed to this report.