"Targeted killing operations must be broadened, not only against those who fire rockets but against their leaders," Infrastructure Minister Benjamin Ben Eliezer told public radio, one day after a rocket killed a woman in Israel.
Palestinians call such attacks by Israel assassinations.
Ben Eliezer, who belongs to the country's influential security cabinet, was making a direct allusion to leaders in prime minister Ismail Haniya's ruling Hamas movement, whose armed wing claimed to have fired rockets on Wednesday.
"They should be tracked night and day. We will make them see this is deterrence," he said.
"If the rockets do not stop, they (Hamas leaders) will have no respite, from the prime minister to the last of them," Ben Eliezer warned.
A 57-year-old mother of two was killed and two other people seriously wounded in the southern Israeli town of Sderot on Wednesday in a salvo of Palestinian rockets fired from the Gaza Strip.
After talks with army top brass Israeli Defence Minister Amir Peretz has vowed that the militants would "pay a heavy price".
"We will move against those who are involved in the firing of rockets, starting from their leaders and down to the last of their terrorists," he said.

Copyright AFP (Agence France-Presse), 2006