The statement described the attack as a ‘blessed invasion of one of the dens of infidels and vice in Muslim Tunisia’ and appeared on a forum that carries messages from the group.
The statement added that there were two attackers and that they weren't killed until they ran out of ammunition.
“Wait for the glad tidings of what will harm you, impure ones, for what you have seen today is the first drop of the rain,” the statement said promising further attacks.
IS, which is based in Syria and Iraq, has affiliates in neighbouring Libya, where many Tunisians have gone to fight and train with extremist groups.
Earlier this week, a prominent Tunisian field commander for IS was killed in fighting inside Libya.
Tunisia's government, meanwhile, announced the arrest of nine people four of whom were connected directly to the attack and five others who supported them elsewhere in the country, authorities said.
The attack on the museum, which houses Roman artefacts, was the worst Tunisia has seen in years.
The deaths of so many tourists prompted a leading Italian cruise ship line to announce Thursday it was cancelling all stops in Tunisia indefinitely.
Prime Minister Habib Essid said that Tunisia was working with other countries to learn more about the slain attackers, identified as Yassine Laabidi and Hatem Khachnaoui.
He said Laabidi had been flagged to intelligence, although not for “anything special.”
Image: Police officers stand guard outside the parliament building in Tunis. Photograph: Zoubeir Souissi/Reuters
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