The claim came as American investigators scrambled to understand the motive for the worst shooting in living memory on US soil, leaving 58 dead an 515 injured.
But IS experts are sceptical that the 64-year-old was linked to the terror group.
The FBI said it had so far found “no connection” between him and any international terrorist group.
Paul Cruickshank from the US-based Combating Terrorism Center said: “ISIS in recent months has made a number of demonstrably false claims for attacks and incidents that had no jihadi terror nexus.”
One theory is that, as the extremists face military defeat on the territory they once held in Iraq and Syria, they are seeking to generate publicity to show they are still a force to their supporters.
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Mr Cruickshank added: “ISIS, desperate for attention, will claim just about anything these days knowing their supporters won’t believe the government or media.”
French Interior Minister Gerard Collomb made the same point on Tuesday, saying the group “tended to claim every attack” in order to “maintain a presence in the media space.”
Islamic State specialist Shiraz Maher wrote on Twitter that if the Las Vegas shooter “is a convert and made contact with ISIS, someone would have to know. Friends, family, law enforcement will shed light on that.”
Earlier this week, ISIS released a chilling video bragging that the Las Vegas shooting massacre was revenge for US attacks against the caliphate.
ISIS accuses America of “being at the forefront of the aggression towards the Islamic State”.
The group warns “we are an Islamic army that has been accepted by a large number of Muslims worldwide, so effectively any aggression towards IS is aggression towards Muslims from all walks of life”.
The video also blames US President Donald Trump for ignoring their previous warnings.
ISIS’s Amaq news agency, said: “The Las Vegas attack was carried out by a soldier of the Islamic State and he carried it out in response to calls to target states of the coalition (in Iraq).”
In a later statement from ISIS, the militant group referred to the Las Vegas attacker by the name of “Abu Abd al-Bar al-Ameriki”.
US authorities said the gunman, who lived in a retirement home in Mesquite, Nevada, was armed with more than 10 rifles, and opened fire on a Las Vegas country music festival on Sunday night from a 32nd-floor hotel window.
The gunman killed himself before police entered the hotel room he was shooting from, police said.
Authorities have yet to identify a motive for the shooting.