It was the fourth straight day of airstrikes and rocket attacks amid efforts to agree on a cease-fire.
More than 200,000 schoolchildren remained at home as a safety precaution, officials said.
Egypt sought to broker a truce between Israel and Gaza militant groups and U.N. meetings were to begin on reviving talks aimed at negotiating a Palestinian state.
The Israeli Air Force conducted six strikes in Gaza, targeting weapon storage facilities, rocket launchers and cells preparing to fire rockets, Brig. Gen. Yoav Mordechai, army spokesman, told Israel Radio.
More than 160 Qassam rockets and Grad missiles have been fired at southern Israel since the recent round of violence erupted Friday.
"Until now we have killed 20 armed terrorists, and a 12 year-old boy who was walking near where Islamic Jihad terrorists were about to fire rockets," Mordechai said.
He confirmed that Egypt is attempting to mediate a cease-fire but said as long as rockets are fired at Israel "we will respond."
Mordechai said Israel would halt its military actions if the rocket fire ceases but would continue pre-emptive operations to foil terror-attack plans.
The military "will continue to protect Israeli citizens and will strike all those who rise to attack us," Israeli Radio quoted Defense Minister Ehud Barak as saying. "Those who attack our civilians will be punished."
The recent round of violence erupted after the Air Force killed Zuhair al-Qaissi, a commander of the Palestinian Resistance Committee in Gaza who planned to wage a large-scale attack on Israel's border with Egypt.
Hamas, the Palestinian Sunni Islamic political party governing the Gaza Strip, said on television Israel told Egypt it would stop airstrikes on Gaza at midnight Monday, Israel Radio reported.
The Islamic Jihad and Popular Resistance Committee in Gaza claimed responsibility for the rocket attacks, but Israel holds Hamas responsible for the upsurge in violence.
Palestinian National Authority President Mahmoud Abbas discussed cease-fire prospects with Hamas Chairman Khaled Mashaal, Palestinian Islamic Jihad Secretary-General Ramadan Shallah and Arab League Secretary-General Nabil al-Araby, the authority said.
Israeli Deputy Ambassador to the United Nations Haim Waxman sent a letter calling on Secretary-General Ban Ki-moon and Security Council members to "unequivocally condemn" the Palestinian militant groups' attacks on Israel and to do everything in their power to "stop the rocket fire that continues to rain down on Israeli civilians, in violation of every precept of international law."
Ban and the Security Council had no immediate comment.
Chief Palestine Liberation Organization negotiator Saeb Erekat blamed Israel for the escalation and called on Washington to halt the Israeli military operations and help restore calm.
Washington had no immediate comment.
Erekat, part of a Palestinian team negotiating with Israel to establish a Palestinian state, also appealed to the United Nations, the European Union and Russia -- which along with the United States make up the Quartet of Middle East negotiators -- to get Israel to stop the airstrikes.
The Quartet was to meet with Ban at the United Nations Monday to discuss how to revive the stalled peace talks.
The Quartet, which last met in September, seeks to reach a negotiated solution by the end of this year to create a legal Palestinian state.
Celebrity Couples of 2014 [PHOTOS]