The rockets caused no damage or casualties.
The incident is the second within the space of a month after four missiles were fired towards the Israeli Red Sea city of Eilat, suggesting an increase in tensions on Israel's southern border.
"This morning projectiles launched from Sinai hit an open area in southern Israel".
In a statement on social media, the group said it had fired two Katyusha rockets at "southern Palestine", according to the Walla news site. They fell within the area of the Eshkol Regional Council, bordering the Gaza Strip and the Sinai. "No injuries have been reported".
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The IDF has not commented on the claim, but the Israel is reported to have carried out drone strikes "with Egypt's knowledge and blessing" against militants in the restive peninsula.
The attack was launched after the Israeli Air Force attacked an ISIS terrorist base in Sinai, earlier in the day. Three of the four were intercepted by Israel's Iron Dome missile defense system. The group said it had been launched "in order to teach the Jews and the crusaders a proxy war will not avail them of anything", and threatened future "calamitous" attacks. According to the Guardian, Hamas accused Israel of killing two Palestinians in Egypt's Sinai region via an airstrike.
The IS has been in a vicious conflict with the Egyptian military in the Sinai for years.
Bashat asserted that Israel will not be able to respond to the rockets fired from Sinai against its territories because of the peace treaty signed in 1979.