Military officials and experts warned that the militant Hamas group, with the help of Lebanese Hezbollah guerrillas, has managed to increase the range and deadliness of the rockets.
A new threat from Gaza could complicate Sharon's plan to withdraw from the coastal strip by September 2005. More rocket attacks could undercut popular support for the plan.
Sharon visited Sderot, a working-class town two miles from Gaza, to try to reassure panicked residents. While he visited a community center, three rockets fell more than a mile away. It was not clear if the militants were aware of Sharon's presence.
The prime minister promised "wide-ranging actions to ensure that what happened here yesterday will not recur," but was met with skepticism.
"I want to ask you how it can be that a child goes to nursery school and doesn't come home again, how?" Yitzhak Ohayon, the father of the boy killed Monday, asked a grim-faced Sharon.
"This is the most terrible thing that could happen," replied Sharon. The prime minister lost one of his sons in a shooting accident when the boy was 12.
"There is no cure for this pain, which will follow you all your life," Sharon said.
In the Gaza Strip, Israeli tanks encircled the town of Beit Hanoun, home to 21,000 Palestinians. Bulldozers tore up the main road in the eighth major Israeli military operation there since the outbreak of fighting in 2000.
Troops advanced about 700 yards into town, meeting no armed resistance, only sporadic stone-throwing by teenagers, residents said. A local hospital said 17 of the youngsters were wounded by army fire, one critically.
Beit Hanoun resident Ramadan Shabat, 39, said he had stocked up on supplies after Monday's deadly attack on Sderot.
As he spoke by telephone, machine gun fire could be heard in the background, and he said that at one point bullets hit one of his windows. He said bulldozers were digging up the street outside his home, and that a sewage pipe had been broken.
