There were no casualties from the rockets, though one projectile landed near a kindergarten in a community near Gaza, police spokesman Micky Rosenfeld said. Warning sirens sent residents scrambling for shelter. The Israeli offensive was aimed at halting years of rocket attacks, and the military declared a cease-fire on January 18 after declaring its goals had been achieved.

But Sunday’s rockets, which followed sporadic rocket fire and the killing of an Israeli soldier in a border bombing attack last week, illustrated the difficulties of achieving a complete end to the attacks. Despite years of efforts, Israel’s high-tech military still has not found a solution to stopping the crude, homemade projectiles.

Speaking to his Cabinet on Sunday, Israel’s outgoing prime minister, Ehud Olmert, said the rocket fire had now “climbed to a level” that requires Israel to respond. “We shall not signal in advance to the terrorists how we are going to respond, where we are going to respond or when we are going to respond, but we shall respond,” Olmert said.

Hamas has not taken responsibility for any of the new attacks, which have been claimed by smaller militant groups. But Israel says it holds Hamas, which has ruled Gaza since seizing power in June 2007, responsible for all attacks emanating from Gaza.

The rocket strikes come just over a week before Israel holds a parliamentary election, and could influence the outcome by making the Gaza offensive appear less successful. That could erode support for candidate Tzipi Livni, the foreign minister and one of the leaders behind the operation. Livni has replaced Olmert as head of the centrist Kadima party and is the only serious challenger to the front-runner, hardline Likud leader Benjamin Netanyahu, according to opinion polls.

Netanyahu has been campaigning on a hardline platform that calls for a tough stance against Hamas, and he stands to benefit if Israelis conclude that the offensive failed to achieve its goal of making residents of southern Israel safer.

Since ending the offensive, Israel has conducted retaliatory strikes and pounded tunnels Hamas uses to smuggle in weapons from Egypt. Israeli forces have also shot and killed three men who Palestinians identified as farmers along the Gaza-Israel border.

One of Israel’s concerns is that Hamas could continue smuggling weapons into Gaza through tunnels under the Egypt border. The smuggling allowed the group to obtain longer-range rockets that now have about one-eighth of Israel’s population in range. Israel is pushing Egypt to do more to crack down on the flow of weapons, and internationally backed anti-smuggling efforts are at the center of attempts to win a lasting cease-fire in Gaza.

Gaza is struggling to recover from the three-week offensive, which left about 1,300 people dead. Thirteen Israelis were killed, including three civilians.