Rocket fire has continued sporadically with retaliatory air strikes but there are no reports of casualties.
Rocket fire is again hitting the Green Zone, along with an military base in the city.
Previously, Hamas officials have said they were trying to rein in rocket fire from Gaza.
Rocket fire from Gaza has dropped sharply since Israel's devastating 22-day offensive in December 2008.
Israel's aim was to stop Palestinian rocket fire to nearby towns in southern Israel.
And de-escalation has to begin with, again, an end to rocket fire from Gaza.
Israel retaliated by firing toward the source of the rocket fire, the IDF spokesman said.
We believe that the precipitating factor for the conflict was the rocket fire coming out of Gaza.
Two militant groups said this week's deadly rocket fire into Sderot was, quote, revenge for Beit Hanoun.
Earlier this week, an Israeli woman was killed by rocket fire, the first such fatality this year.
Gaza rocket fire on Israel has declined since a military campaign in November, but sporadic attacks persist.
The stated Israel aim is to deal a blow to Hamas and prevent or reduce rocket fire.
Along with the airstrikes, Israel responded to Saturday's rocket fire by closing the Kerem Shalom crossing with Gaza.
The Israeli military says it was targeting only Hamas militants, blaming them for rocket fire into southern Israel.
But angry Palestinians, like 28-year-old Sousa Nasir, say the rocket fire on southern Israel will only increase now.
For the Israelis, their goal is a halt to the rocket fire and a lengthy period of calm.
BBC: International support for attack on Gaza in the balance
The results of this air strike underscore the difficult challenge Israel's army faces in responding to the rocket fire.
Rocket fire has been rare since an informal cease-fire was reached last November.
If the rocket fire continues, it will have to find a military answer.
And rocket fire, apparently from the Free Syrian Army, has landed in Shiite areas around the Lebanese town of Hermel.
The rocket fire is coming from Sadr City, the Shiite enclave mostly controlled by the militia leader and cleric Moqtada al-Sadr.
Israel began the offensive in response to rocket fire by Hamas militants after showing eight years of restraint, the officer said.
CNN: Palestinians: 1,300 killed, 22,000 buildings destroyed in Gaza
Wars, intifadas, terror, rocket fire, Hamas in Gaza, Hezbollah in Lebanon, hostility in the U.N. and Europe, threats of boycotts and delegitimatization.
No Israelis have been killed this year by the Gaza rocket fire.
The Israeli military says its aircraft have targeted Palestinian militant sites in the Gaza Strip in response to continued rocket fire on southern Israel.
Secretary General Ban Ki-moon has roundly condemned both sides: Hamas for the rocket fire and Israel for its "excessive use of force" in retaliating.
"There's no guarantee even if Hamas is removed from power in Gaza that rocket fire will not continue, " says Nicolas Pelham of the ICG.
There was rocket fire coming from Sadr City to a U.S. military base and the to Green Zone that killed three U.S. soldiers, injured 31.
Israeli officials say the goal of the incursion was to hit the terrorist infrastructure in Gaza and halt Palestinian rocket fire at nearby Israeli towns.
In a potential repeat of the rocket attacks on Sderot, Israeli towns near the West Bank would be highly vulnerable to increased Qassam rocket fire.
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