Shin Bet security service chief Yuval Diskin told a Cabinet meeting that the rockets could also hit Kiryat Gat and Ashdod, cities that had been considered far beyond Hamas's firing range, Haaretz reported Sunday.
"We believe that if we strike at significant assets, they will respond with longer-range fire," Diskin said.
Diskin's comments came the same day that 11 rockets were fired by Palestinians from the Gaza Strip landed in the Negev desert region, officials said.
Mortars were also fired, with one shell aimed at the Ashkelon Coast Regional Council slightly injuring a foreign worker hit by shrapnel while working in a greenhouse. He was evacuated to the Barzilai Medical Center in Ashkelon, Ynetnews.com reported.
Following the rocket barrages, Israeli air force jets struck a launcher near the northern Gaza Strip town of Beit Hanoun, officials said.
A Palestinian source told Ynetnews.com the rocket fire was meant as a protest against Israel's policy of blockading Gaza entry points.