ISIS' claim, made in a statement posted to Twitter, cannot be independently verified by CNN. But it boasted about the first major terrorist attack of 2017.
"In continuation of the blessed operations which ISIS carries out against Turkey, a soldier of the brave caliphate attacked one of the most popular nightclubs while Christians were celebrating their holiday," the statement read.
Both Turkish and US officials have called the attack an act of terrorism.
Here's the latest on the investigation, the victims and why Turkey keeps getting targeted:
Investigators have found the fingerprints of the suspect and know what he looks like, Deputy Prime Minister Numan Kurtulmus said Monday.
Eight people have been detained in connection with the attack, Kurtulmus said, but the suspect was not among them.
"We will find him, no delay," Turkish Prime Minister Binali Yildirim said.
Footage of the attacker showed him shooting a security guard and police officer at the entrance of the nightclub. Turkish authorities said they believe he carried out the attack alone.
Earlier Monday, the militant Kurdistan Worker's Party, or PKK
, distanced itself from the attack.
"No Kurdish forces have anything to do with this attack," the PKK said. "The Kurdish freedom fight is also the fight for democratization of Turkey. That's why we won't target innocent and civilian people."
Those killed in the attack were from 14 countries
, including India, Morocco, Jordan, Canada, Russia, Tunisia, Saudi Arabia and Kuwait.
Security guard Fatih Cakmak was one of the first victims killed. He had considered himself lucky after surviving a December attack outside Istanbul's Vodafone Arena
, where he was also working security.
"He went to work, and now he's gone," said his father, Hassan Cakmak, who said he can't believe he survived his 32-year-old son.
Lubna Ghaznawi, a young female entrepreneur from Saudi Arabia, was also killed. The 34-year-old worked full-time as a communications manager for one of Saudi Arabia's largest banks and also co-owned a start-up with her sister called Exclusave Card, the first student discount card in Saudi Arabia.
"She was an optimist and loved going to new places," her friend Seham al-Shahrani told CNN. "Laughter and happiness filled whatever place she went to."
Dozens of people were hospitalized. As of Monday, 46 were still being treated, including one American, according to the Istanbul governor's office. A handful of the injured were in critical condition.
'We were having fun'
Witnesses described how the festive evening turned into a bloodbath.
"We were having fun. At first we thought it was a fight, then there was a lot of gunfire," witness Yunus Turk told CNN
"After the gunfire everyone started to run toward the terrace. We ran as well. There was someone next to me who was shot and fell on the floor. We ran away and hid under the sofas."
Another witness said he didn't know how many attackers there were, but he saw one person and hid.
"I got shot in the f****** leg, man," he told journalists as he was taken into an ambulance. "These crazy people came in shooting everything."
On Sunday, the club issued a statement on its Facebook page
"This terrible incident is a terror attack against our citizens' peace, brotherhood, serenity, economy, tourism and against our nation," the statement read.
"Our hearts bleed and the bullets are in our heart."
Why Turkey keeps getting targeted
Turkey's deputy prime minister said he believes the attack was committed in response to Operation Euphrates Shield
, Turkey's ground operation against ISIS in Syria.
But the country is "fighting a two-front war -- against the Kurdish Workers' Party, and against the Islamic State," CNN intelligence and security analyst Bob Baer said.
Turkey shares a 500-mile (800-kilometer) border with Syria, making it relatively easy for ISIS fighters and supplies to cross.
"That border is so porous -- weapons, explosives, people coming across it," Baer said.
Both ISIS and Kurdish militants have launched attacks in Turkey, which is also reeling from a bloody and failed military coup
ISIS has typically refrained from claiming responsibility for attacks in Turkey to create "an environment of suspicion in Turkish politics," analyst Soner Cagaptay
wrote for CNN last year.
So ISIS' claim of responsibility for Sunday's nightclub attack could mark a turning point.
"I think with Istanbul, it's a declaration of war on Turkey," Baer said.
Meanwhile, Turkish security forces clash almost daily with rebel PKK militants, mostly in predominantly Kurdish parts of southeastern Turkey.
In December, a pair of bombings in Istanbul
killed 44 people and wounded 155 others in an attack by a breakaway group of the PKK. The two explosions occurred after a heavily attended soccer game at Besiktas Vodafone Arena.
Also in December, a car bomb exploded
near a public bus, killing 13 soldiers in the central province of Kayseri. Three days later, a gunman assassinated Russia's ambassador
to Turkey at an Ankara art gallery.
'The issue of a copycat'
So how could the attack at the Reina nightclub have implications elsewhere?
Since the assailant used a gun, and apparently started by killing the security guard, a similar attack could happen anywhere, CNN senior law enforcement analyst Tom Fuentes said.
"You have the issue of a copycat," he said. "So here in the United States, we have over 300 million guns at large in our population. So we're talking about one person getting a hold of one of those guns and launching an attack and doing it on his own. ... So it's almost impossible to stop, if that's what we end up with -- a lone wolf who wants to get a gun."