The early morning airstrike in the eastern Gaza Strip came hours after Hamas' armed wing threatened Israel over the attacks.
The Israel Defense Forces had no immediate comment on the latest bombing, which also left three people wounded, according to the Palestinian sources.
Israel "will pay the price" for its actions in Gaza, said Abu Obaida, spokesman for the Izzedine al Qassam Brigade of Hamas, the Islamist movement that controls the Palestinian territory of Gaza.
"The Palestinian resistance is capable of selecting its options at this time and all the time," Obaida said. "The Palestinian resistance has what will hurt the Zionist occupation and will not stand on the side and watch."
Israel said the airstrikes are a response to more than 90 rocket attacks from Gaza into southern Israeli communities that injured at least four people.
The military targeted "part of the terror infrastructure used to execute attacks via the Sinai Peninsula, and the Israel-Egypt border, while violating Egyptian sovereignty," the Israel Defense Forces said in a statement.
The forces remain on high alert, with aircraft patrolling the region and targeting suspected militants. The IDF said it "will respond with strength and determination against any attempt to execute terrorist attacks."
Four Israeli military tanks entered some 100 meters into the Gaza area, Palestinian officials in Gaza said Saturday.
Israeli Prime Minister Benjamin Netanyahu spoke with the leaders of the communities that were targeted -- Be'er Sheva, Ashdod, Ashkelon, Kiryat Malakhi, Gan Yavneh, the Eshkol Regional Council, the Sha'ar Hanegev Regional Council and the Bnei Shimon Regional Council -- and praised the residents' fortitude. The town mayors said Israel's Iron Dome air defense system provided security to the residents, according to the prime minister's office.
"We will continue to hit whoever plans to attack citizens of the State of Israel. At the same time, we will continue to improve home front defense including by means of additional Iron Dome systems, the effectiveness of which was shown again over the weekend," Netanyahu said.
U.S. State Department spokeswoman Victoria Nuland condemned "in the strongest terms" the rocket fire from Gaza into southern Israel.
"We call on those responsible to take immediate action to stop these cowardly acts," she said in a statement Saturday.
Palestinians roundly condemned the Israeli actions, which also left at least 25 people wounded.
"Israel's escalation creates a negative atmosphere and increases the tension, which leads to the increase in violence in the region," Palestinian Authority spokesman Nabil Abu Rudaina said.
Talal Abu Tharifa, a member of the political bureau of the Democratic Front for the Liberation of Palestine, urged the Arab League to ask the U.N. Security Council to stop the "aggression." He also wants Israeli military and political leaders to go before the International Criminal Court.
Fawzi Barhoum, a Hamas leader and spokesman, said Israel's actions are intended to cover up the government's activities, such as settlement construction.
The initial airstrike, on Friday afternoon, killed two people in Gaza.
One of the dead was Zuhair al-Qaisy, secretary-general of the Popular Resistance Committees, a militant group that has launched rockets toward Israel and fired mortars from inside Gaza.
The other was Mahmoud Ahmad Al-Hanini, a Hamas military leader originally from the northern West Bank city of Nablus. Al-Hanini was deported to Gaza about five years ago after being freed from an Israeli prison.
Three others members of the Popular Resistance Committees were killed -- two in an Israeli airstrike on a motorbike south of Gaza and one on a motorcycle in Rafah, officials said.
Israeli forces also struck an apparent rocket-launching site in Gaza, killing three. Another airstrike hit a house in Beit Lahia, killing two and wounding others, medical and Palestinian officials said.
Israeli forces say al-Qaisy helped orchestrate an August attack that left 40 people injured, coordinated rocket attacks against Israel and transferred funds from Hezbollah to militant groups in Gaza.
After his death Friday, the Popular Resistance Committees vowed a "seismic response" and said Israel "has opened the doors to hell and the continuous revenge ... will be by the size of this heinous crime."
European Union foreign policy chief Catherine Ashton urged both sides to "avoid further escalation" and "re-establish calm."
"I very much deplore the loss of civilian life," she said in a Saturday statement.