Gaza City (CNN) -- The Palestinian group Islamic Jihad announced an immediate cease-fire with Israel on Sunday following a sharp rise in violence in the past several days.
Islamic Jihad "will cooperate with the cease-fire, but maintains our right to resist the aggression," a spokesman for the military wing of the group told CNN. It said calm "will depend upon the behavior of the occupation," a reference to Israel.
The deal was brokered by Egypt, said Abu Ahmed, as the Islamic Jihad representative refers to himself.
Israel did not immediately confirm whether there had been a deal, which Islamic Jihad announced hours after the Israeli Air Force struck several sites that it suspected were "terror centers" Sunday.
U.N. Secretary-General Ban Ki-moon condemned rocket fire from Gaza and called for it to stop, his spokesman said in a statement Sunday.
Ban "hopes that both parties will fully respect the calm as brokered by Egypt," the statement said, and also "urges maximum Israeli restraint following the killing of a reported 10 alleged militants."
Rocket fire from Gaza continued into late Sunday night, according to the Israel Defense Forces, which said in a statement early Monday that the Israeli air force responded with an airstrike on the suspected militants.
Israeli Prime Minister Benjamin Netanyahu said Sunday that Israel would target anyone who attempts to fire more rockets.
"It is not worthwhile for anybody to test our determination to invoke the government's defense principles. We will prevent every attempt to shoot at Israel, and we will hurt everyone who nevertheless succeeds at doing so," Netanyahu said at the opening of a medical school in northern Israel. "We have no desire (to see) deterioration in the situation but will defend ourselves according to these principles."
The Israeli air force said its Sunday attacks targeted three suspected rocket launching sites and one "terror tunnel" in northern Gaza; and two "terror activity" sites in southern Gaza, as the wave of back-and-forth attacks between the Israeli military and Palestinian militants continued.
No one was hurt in Sunday's attacks, security forces in Gaza said.
On Saturday, at least 10 people were killed in Gaza and southern Israel.
Saturday's violence began when two Islamic Jihad commanders were among seven militants killed by Israeli strikes targeting a training camp in Rafah, Gaza, a spokesman for the militant group and medical sources reported.
The Israeli military said more than 20 mortars and rockets were subsequently fired into their territory. A 55-year-old man was killed in the rocket attacks and 20 others were injured, according to Zaki Heler, an emergency services spokesman in Israel.
Palestinian medical sources told CNN that two people were killed in a second wave of Israeli airstrikes, launched in response to these rocket attacks.
According to Abu Ahmed, the Islamic Jihad spokesman, the original Israeli strikes occurred during a graduation ceremony. Two other members of his organization were injured in that attack, he said. Witnesses reported that at least 10 other people were wounded.
Clashes have been ongoing since Wednesday when Islamic Jihad launched a rocket into Israeli territory.
Israel's representative to the United Nations said he'd written a letter to Ban and the UN Security Council "alerting the international community about the dangerous potential for civilian casualties" as violence escalates in Gaza.
"The council did not utter a single word of condemnation," Ambassador Ron Prosor said in a statement Saturday. "Today one Israeli civilian was murdered and others lay injured in hospitals this evening as a result of the escalating rocket fire -- and we still only hear silence from the Security Council."
On Sunday, the Israeli military said 20 more rockets and mortars were fired into Israel overnight. Officials closed schools and universities within 40 kilometers (24 miles) of the border with Gaza, except for schools in Sderot which are protected against attacks with heavy concrete walls.
Netanyahu said Sunday that Hamas, which controls Gaza, is responsible for maintaining security and preventing rockets from being fired out of Gaza, "even if the executors are from Islamic Jihad."
CNN's Kevin Flower and Richard Roth and journalist Talal Abu-Rahmi contributed to this report.