A statement on its affiliated Amaq news agency said that an IS “fighter” was responsible.
NBC News reported that Mateen had called the emergency services before the attack and swore allegiance to IS.
The gunman was killed in an exchange of fire with 11 police officers, after taking hostages at the club.
US media have published pictures of the suspect, Omar Mateen
The attack is the worst mass shooting in recent US history.
Eight of the victims have so far been named: Edward Sotomayor Jr, Stanley Almodovar III, Luis Omar Ocasio-Capo, Juan Ramon Guerrero, Eric Ivan Ortiz-Rivera, Peter O Gonzalez-Cruz, Luis S Vielma and Kimberly Morris.
A moment of silence was observed across the US at 18:00 local time (22:00 GMT).
In an apparently unrelated event, a heavily armed man was held on weapons and explosive materials charges in southern California after saying he wanted to go to a gay pride event in Los Angeles.
Gun control
Mr Obama said the “brutal murder of dozens of innocent people” was a further reminder of how easy it was to acquire a deadly weapon in the US and shoot people.
“We have to decide if that’s the kind of country we want to be,” said the president, who has campaigned for stricter gun laws. “To actively do nothing is a decision as well.”
He added that it was a heartbreaking day for the LGBT community, and that an attack on any American was an attack on all.
The attack is the worst mass shooting in recent US history.
Eight of the victims have so far been named: Edward Sotomayor Jr, Stanley Almodovar III, Luis Omar Ocasio-Capo, Juan Ramon Guerrero, Eric Ivan Ortiz-Rivera, Peter O Gonzalez-Cruz, Luis S Vielma and Kimberly Morris.
A moment of silence was observed across the US at 18:00 local time (22:00 GMT).
In an apparently unrelated event, a heavily armed man was held on weapons and explosive materials charges in southern California after saying he wanted to go to a gay pride event in Los Angeles.
Gun control
Mr Obama said the “brutal murder of dozens of innocent people” was a further reminder of how easy it was to acquire a deadly weapon in the US and shoot people.
“We have to decide if that’s the kind of country we want to be,” said the president, who has campaigned for stricter gun laws. “To actively do nothing is a decision as well.”
He added that it was a heartbreaking day for the LGBT community, and that an attack on any American was an attack on all.
Orlando police say the life of one of their men was saved by his Kevlar helmet
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