Gaza City (CNN) -- Israel launched fresh airstrikes early Monday in Gaza, security officials and medical sources said, as talks about a possible cease-fire after three days of bombing apparently failed. At least 30 people were injured, including one critically, they said.
A spokeswoman for the Israel Defense Forces confirmed the overnight strikes, saying they were "an indirect response to the firing into the Israel community in the south." The strikes targeted a weapons storage facility and five rocket launching sites in the Gaza Strip, the spokeswoman said.
At least 18 people have been killed since Friday in the strikes, while at least 65 people have been wounded.
Two civilians, including a 13-year-old boy in Gaza, were killed Sunday, Palestinian medical sources said.
The airstrikes are a response to more than 100 rocket attacks from Gaza into Israel since Friday, Israel says.
Eight Israelis have been wounded and 500,000 have been forced into shelters, Israeli military and emergency services said.
An Israeli military aircraft targeted a suspected terrorist moments before he fired a Grad rocket at the city of Ashdod, the Israel Defense Forces said in a statement. The individual had also fired a Grad rocket into Ashdod earlier in the morning, the IDF said.
"The IDF is prepared to defend the residents of Israel and will respond with strength and determination against any attempt to execute terrorist attacks," the statement said.
The IDF generally does not comment on other reported casualties in such incidents.
Israeli Prime Minister Benjamin Netanyahu suggested Sunday that the new cycle of attacks and counterattacks resulted from a successful Israeli strike on "an arch-terrorist who organized many attacks against the state of Israel."
Two people were killed in that strike: Zuhair al-Qaisy, secretary-general of the Popular Resistance Committees, and Mahmoud Ahmad Al-Hanini, a Hamas military leader.
"Naturally, this led to another round with the Popular Resistance Committees, Islamic Jihad and other groups," Netanyahu said, naming Palestinian militant groups.
Israel's military "is striking at them in strength. ... We have exacted from them a very high price; naturally, we will act as necessary," Netaynahu said.
Palestinian factions met Sunday to discuss the possibility of a truce to be implemented Sunday night, according to a spokesman for the Salah Edeen Brigades, one of the militant factions. Hamas leadership in Gaza and Egyptian officials were working to trying to bring about a truce, said the spokesman, who goes by the name Abu Muhamad.
However, Islamic Jihad rejected the possibility of a truce until certain conditions are met, including an end to the airstrikes and "targeted assassinations," according to the militant group's official radio station.
The IDF statement Sunday warned that groups that "carry out terror attacks against the state of Israel will bear the consequences of these actions in any future operation embarked upon by the IDF. The Hamas terror organization is solely responsible for any terrorist activity emanating from the Gaza Strip."
Palestinians named Sunday's child victim as Ayuub Assilla.
He was killed near the Jabalia refugee camp, north of Gaza city.
The other victim was a 60-year-old Palestinian man who was guarding a farm grove in Gaza City, Palestinians said.
They were the second and third civilians killed in the weekend's violence, after a 51-year-old man was killed on the back of a motorcycle on Saturday. The other victims have been militants, according to Palestinian sources.
Foreign Minister Avigdor Liberman said Israel makes its "best effort to target terrorists and not the civilian population," but added: "We will not accept the constant disruption of life in the south of Israel, and I advise all heads of terror to think well about their actions."
He blamed Hamas, the Palestinian Islamist movement that runs Gaza, and Palestinian Authority President Mahmoud Abbas for the violence.
"Abbas must decide if he wants to conduct serious negotiations for peace or align himself with Hamas and Islamic Jihad and become a part of the map of world terror," Liberman added.
He was referring to ongoing talks between Abbas' Fatah faction and Hamas, aimed at forming a new Palestinian unity government. The two factions have been bitter rivals since Hamas seized control of the Gaza Strip in 2007.
A total of 130 rockets have been fired into southern Israel since Friday, the IDF said. Ninety-three landed in Israel, while 37 were shot down by Israel's Iron Dome missile defense system, the IDF said.
Israel closed schools Sunday in the southern part of the country as precaution.
Palestinian officials accused Israel of trying to disturb a "truce" that was already in place. But despite efforts to bring about a truce over the years, rocket attacks have continued from Gaza.
Both sides sent dueling letters to the U.N. Security Council on Sunday, calling for an end to the violence.
Mustafa Barghouti, a Palestinian lawmaker in the West Bank, slammed a "provocation that is planned in cold blood by Israel to undermine the cease-fire in Gaza and to undermine the nonviolent nature of the Palestinian struggle today."
Hanan Ashrawi, executive committee member of the Palestine Liberation Organization, accused Israel of "targeting of isolated civilians through air strikes and targeted assassinations."
She insisted Netanyahu was seeking "to provoke the Palestinian side by dragging them to the circle of violence and destabilize the stability of the region and violate the truce agreement which the Palestinian factions committed to."
"Nothing could be further from the truth," responded Mark Regev, spokesman for Netanyahu. He said instability was being wrought by "Iran and its allies in Gaza who have been shooting scores of rockets at Israeli civilian population centers, at townships and at cities.
"I would hope that Dr. Ashrawi would unequivocally condemn the deliberate targeting of innocent civilians by the terrorists in Gaza."
On Saturday, Abbas called on international leaders to bring a stop to the attacks. However, Hamas' armed wing threatened Israel over the attacks.
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.
European Union foreign policy chief Catherine Ashton urged both sides to "avoid further escalation" and "re-establish calm."
CNN's Kamal Ghattas, Talal Abu Rahma, Guy Azriel, Kevin Flower, Kareem Khadder and Josh Levs contributed to this report.