Sunday's shootings were the bloodiest in Jordan in recent memory and raised new concerns about the rise of Islamic militancy in the pro-Western kingdom.
Jordan plays a key role in the U.S.-led military campaign against IS, which seized large areas in neighboring Iraq and Syria in 2014 and proclaimed a "caliphate" there.
The shootings took place in the central Jordanian town of Karak. Hours after an initial attack on a police patrol, four gunmen were shot and killed by Jordanian security forces during a standoff at Karak Castle, a Crusader fortress and popular tourist destination.
The IS claim was published Tuesday on "Shumoukh al-Islam," a password-protected website affiliated with the extremist group.
The statement said that "four soldiers of the caliphate" armed with machine guns and hand grenades carried out the attacks, killing 10 "apostates." It said the four IS fighters were engaged in "fierce clashes lasting several hours" with Jordanian forces before being killed.
The statement threatened more attacks in anti-IS coalition member states. "We promise the Crusader coalition countries something worse and more severe, Allah permitting ...," it said.
Jordanian officials have refused to identify the attackers.
Seven members of the Jordanian security forces, two local bystanders and the Canadian tourist were killed in the attacks which also left 34 people wounded.
Jordan has been facing homegrown extremism; hundreds of Jordanians are fighting alongside other IS militants in Iraq and Syria and several thousand more are believed to support the extremist group in the kingdom.
Sunday's shootings were the latest in a series of attacks over the past year that have challenged the pro-Western kingdom's claim to be an oasis of stability in a region increasingly threatened by Islamic extremists.
Earlier this year, IS claimed responsibility for a deadly cross-border attack from Syria on a Jordanian border post.
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