The claim is yet to be confirmed by officials from the Tunisian government or security services.
Two separate attacks hit the country’s capital, Tunis, on Thursday morning.
In the first, a police patrol car was targeted near the French embassy at around 11am.
A police officer was killed and three civilians were wounded in the blast.
At the same time, a second suicide bomber struck one of the entrances of the headquarters to the government’s anti-terrorism brigade on the outskirts of the city.
Four police officers were wounded and heavily armed police cordoned off streets throughout the city.