Tel Aviv - Hamas further deepened its rocket attacks into southern Israel Tuesday, sending two upgraded Russian-type Grad rockets to a distance of more than 30 kilometres, police said.

One rocket struck near the Israeli town of Qiryat Malahi, east of the southern Israeli coastal city of Ashdod which was hit for the first time late Monday.

Another landed near the Bedouin town of Rahat, north of Beersheba, the largest Israeli city in the southern Negev desert.

Hamas said in a statement the rocket had aimed for Beersheba, where Israeli Police Spokesman Micky Rosenfeld said authorities for the first time ever activated a rocket alarm, sending residents into safe rooms and shelters.

He said Palestinian militants fired at least 30 self-made Qassam and other rockets at Israel Tuesday by the late afternoon, bringing to more than 220 the total launched since a deadly Israeli air offensive in Gaza - aimed at curbing attacks from the strip - began Saturday.

Two Israelis were lightly injured when their house in the Israeli town of Sderot, located only a few kilometres from Gaza, suffered a direct hit earlier in the day. A dining room in an Israeli kibbutz, which was empty at the time, was also direct hit. (dpa)