A shaky, partially undeclared ceasefire went into effect overnight Monday between Islamic Jihad rocket squads in the Gaza Strip and Israel, in a bid to end four days of cross-border rocket and retaliation attacks.

"If there are no attacks from Gaza, there is no reason to take action to protect our people," a senior Israeli government source who requested anonymity told Xinhua Tuesday morning.

Also on Tuesday morning, Islamic Jihad announced that they had "officially" accepted the truce, according to Israel's Army Radio.

"Quiet will be met with quiet; fire will be met with fire," Israel Defense Forces (IDF) Chief of Staff Lt.-Gen. Benny Gantz was quoted as saying.

"Our operations will depend on events on the ground," IDF Spokesman Brig.-Gen. Yoav Mordechai said.

"These are 'understandings,' and not signed documents," Israeli Minister of Home Front Defense Matan Vilnai said in a radio interview, adding that "at the moment the direction is toward calm and it appears, unless there are last-minute developments, that this round is now behind us."

The Israeli Prime Minister Spokesman's Office would neither confirm nor deny to Xinhua early Tuesday that an agreement has been reached.

Amos Gilad, who heads the Israeli Defense Ministry's political- military affairs directorate, said in an interview on the extent of the reported cessation of hostilities that "if it's quiet over there (in Gaza), it'll be quiet over here," referring to the Israeli counter strikes.

Despite the reports, an Israeli Defense Forces spokesman told Xinhua that the Palestinians fired three rockets into Israel since Monday night, although there were no reports of injury or damage.

It was also unclear if the three batteries of Iron Dome anti- missile system deployed near southern Israeli cities went into to action to down the projectiles before they hit populated areas.

IDF officials have said that they expect to deploy a fourth battery of Iron Dome in the coming weeks, in order to close potential gaps in coverage by the mobile units currently deployed outside the major populated areas.

About 200 missiles and mortar shells fired from Gaza at the Negev city of Beersheba, coastal Ashkelon and Ashdod as well as other areas since Friday have forced 1 million Israelis to bomb shelters and other protected areas.

The latest round of conflicts started on Friday afternoon when the Israel Air Force struck a car carrying the leader of the Popular Resistance Committees (PRC), Zuhair al-Qaisi, who the Israeli army said was planning a major terror attack on Israel's southern border.

Soon thereafter, Palestinian militants began firing rockets and mortars into Israel, in amounts that, at one point, exceeded those during Operation Cast Lead in December 2008.

Retaliatory airstrikes from Israel killed more than 20 Palestinians, at least 15 of them militants, according to Palestinian officials. Dozens of other Palestinians and Israelis have been wounded in the mutual missile and air attacks.

Some residents in Israel's southern cities and towns in a 40-km radius from the coastal enclave told Xinhua that they finally had their first full night of sleep in four days.

"(I) woke up, realized I had slept through the night with no alarms and no explosions or distant fire, ran to computer and discovered we have a ceasefire! Whew," said Adele Raemer, a resident of Kibbutz Nirim alongside southern Gaza.

Eyes of Barbara Carter, a retired English teacher who moved to Israel from the United States almost a decade ago, got swollen with tears while she described how a neighbor's young daughter clutched her when one rocket salvo hit the southern city of Beersheba.

"Why must children grow up like this?" she said, bursting into tears when speaking to Xinhua.

"She put both arms around my neck, wrapped her legs around my waist and held on for dear life," Carter said, "Now why does she have to grow up with that?"

"I don't cry when I'm scared, I cry when I'm pissed off, and I' m really pissed off right now," she said.

Israeli Foreign Ministry earlier lodged an official complaint with the United Nations Secretary General Ban Ki-moon over the barrages of over 200 Grad and Kassam rockets and mortars fired into Israel.

"These rockets are targeted at civilians -- one of them falling directly on a school. I ask you, Excellency, to picture how different the current situation would be if the children would have been in school all the time the rocket fell," the ministry said.

The PRC and Islamic Jihad have both taken responsibility for some 200 rockets and mortars fired at Israeli cities and towns as of Monday evening, while the Islamic Hamas movement has reputedly stayed out of the fight.

Israel holds Hamas responsible for any hostile acts emanating from Gaza.