The Palestinian resistance group Hamas said firing rockets at the southern city of Dimona was a message from its military wing, the Ezzeddin al-Qassam Brigades, to Israel Anadolu Agency reported
"It shows the weakness and vunrability of the Israeli occupation," Hamas spokesman Sami Abu Zuhri said in an early Thursday statement.
"Our responses [to Israeli strikes] are still in their early stages," he added.
The Israeli army admitted Wednesday that three rockets had been fired from the Gaza Strip at Dimona. No casualties were reported.
Ezzeddin al-Qassam Brigades claimed responsibility for striking Dimona, for the first time.
In a statement, the group announced firing three M75 rockets at Dimona, which is located nearly 65km from Gaza and houses Israel's nuclear reactor.
Meanwhile, at least 68 Palestinians have been killed by Israel since Monday, according to medical sources.
Israel has launched a military offensive - dubbed "Operation Protective Edge" - with the stated aim of staunching rocket fire from Gaza.
It has continued to pound the territory with airstrikes, while ground troops remain massed on the Gaza Strip's borders in advance of a possible ground assault.