Three Kassam rockets were fired at southern Ashkelon Tuesday evening.
The rockets landed in the national park near the industrial zone of the city, causing no casualties. Hamas claimed responsibility for the shooting.
Earlier, the IDF struck at Hamas infrastructure in the Gaza Strip after a barrage of Kassams, killing at least nine terror operatives in joint ground and air operations.
Seven Hamas operatives were killed in an IAF air strike on a Hamas military installation near Khan Yunis in the southern Gaza Strip.
After nightfall Tuesday, army aircraft fired missiles at Palestinian rocket squads in northern Gaza, wounding three people, Palestinian security and hospital officials said.
Palestinian health ministry official Dr. Moaiya Hassanain said the wounded were civilians. The army had no immediate comment.
Regarding the earlier strike, the IDF said it was responding to the firing of four Kassam rockets into Sderot earlier in the day.
On Tuesday morning, IDF troops shot and killed two Hamas gunmen in clashes along the Gaza border.
Islam Shahwan, a spokesman for the Hamas executive force, said the strike hit a station in the southern Gaza village of Abassan, east of Khan Yunis. He said the men had been holding afternoon prayers when the building was hit.
Hamas's response was quick to come: By nightfall, a barrage of more than 10 Kassam rockets pounded Sderot, one of them scoring a direct hit on a home and a factory and wounding three people.
One woman was moderately wounded by the rocket that hit a house, and two other people were lightly wounded. Several others were treated for shock.
The house itself was also reported to be heavily damaged. Power outages were also reported in some parts of the city after one of the rockets hit a power line.
Six more rockets were fired from the Strip later in the evening - one of them landing in Ashkelon - but caused no casualties.
Meanwhile, with security services reporting an increase in motivation to carry out terror attacks following the bombing in Dimona, the Israel Police decided Tuesday to raise the national alert level to "C," the second-highest.
Police said they would concentrate thousands of reinforcements around seam-line communities and in the South, as well as in the Jerusalem and Tel Aviv districts and in crowded areas.
Security officials said Tuesday that the number of intelligence alerts have increased considerably since the attack, with over 50 warnings of different attempts to launch attacks against Israeli targets. Almost a dozen of those warnings were so-called "specific" alerts, pointing to particular targets or locales.
In the 24 hours after the bombing, Border Police units throughout the country arrested 236 Palestinians who had illegally entered Israel to work. Two of them were wanted by the Shin Bet (Israel Security Agency) for questioning.
Three stolen vehicles were also recovered in the operation.
Terrorists often follow the tracks of these illegal workers in evading checkpoints and exiting the West Bank. The unfenced 30 kilometers of the southern edge of the West Bank is a popular crossing spot for workers from the Hebron area, and it is likely that this was the route taken by the Dimona bombers, who security forces believe already had some degree of familiarity with the Negev town.
In previous months, Border Police operations in Dimona have discovered illegal Palestinian workers holed up in local building projects.
Separately on Tuesday, Defense Minister Ehud Barak said Israel would defeat its enemies and that the IDF would succeed in stopping terrorism from the southern Hebron Hills, where security officials estimate the two Dimona bombers originated.
"Just like your parents provided the solutions when they fought in the Jordan Valley, we... will now [find] solutions for the terrorism in Hebron and the Gaza Strip," Barak told cadets in the Officers' Course during an exercise at the Shizafon Base near Eilat.
AP contributed to the report.
