The official, speaking on condition of anonymity, said it had not yet been decided when the lull would take place. Hamas had no immediate comment.
The appeal was made by a United Nations official, the official said, confirming Israeli media reports, shortly after Hamas rejected an Egyptian-proposed ceasefire to end the nine-day war in which 215 Palestinians and an Israeli have died.
The Israeli army also said the killing of four Palestinian children on a Gaza beachfront Wednesday appeared to be the "tragic outcome" of an Israeli strike targeting Hamas militants.
A person stands by the broken window of the Al-Wafa rehabilitation hospital near Gaza City following an Israeli military strike. (AFP photo)
"Based on preliminary results the target of this strike was Hamas terrorist operatives," the military said in a statement. "The reported civilian casualties from this strike are a tragic outcome."
Hundreds of Palestinian families, their children crying, had fled on Wednesday, as Israel intensified airstrikes on Hamas targets, including homes of the movement's leaders, following failed Egyptian ceasefire efforts. Before the renewed bombardment, Israel had told tens of thousands of residents of border areas to evacuate their neighborhoods.
The Palestinian death toll in nine days of fighting rose to 204, with some 1,450 wounded, Palestinian health officials said. On the Israeli side, one man was killed and several people were wounded since the fighting erupted on July 8.
Israeli shelling killed four boys on a Gaza beach on Wednesday, a local health official said. Ashraf al-Qidra of the Gaza health ministry said shelling from an Israeli gunboat off Gaza's Mediterranean coast killed four boys - two aged 10 and the others 9 and 11 - from one family and critically wounded another youngster on the beach. An Israeli military spokesman had no immediate comment.
The renewed bombings came a day after Israel initially accepted an Egyptian truce proposal that called for a halt of hostilities. That was to be followed by talks on the terms of a longer-term cease-fire, including easing Gaza's seven-year-old border blockade by Israel and Egypt.
Hamas rejected the plan and instead launched more rockets at Israel. The militant group views a significant easing of the blockade as key to its survival, but does not believe Egypt's current rulers - who deposed a Hamas-friendly government in Cairo last year - can be fair brokers.
Read: Uproar in Rajya Sabha over fighting in Gaza strip
As Cairo's effort collapsed, Israeli Prime Minister Benjamin Netanyahu warned that Hamas will pay a high price for rejecting the truce offer.
An Israeli official said the defence minister asked Prime Minister Benjamin Netanyahu's security cabinet to authorise the mobilisation of another 8,000 reserve troops. The military has said that around 30,000 reservists have been called up since the Israeli offensive began a week ago.
Israeli experts predicted overland raids in the Gaza Strip to destroy command bunkers and tunnels that have allowed the outgunned Palestinians to withstand air and naval barrages and keep the rockets flying.
The website of the Gaza interior ministry said Israel warplanes carried out dozens of air strikes before dawn Wednesday, targeting 30 houses, including those of senior Hamas leaders Mahmoud Zahar, Jamila Shanti, Fathi Hamas and Ismail Ashkar.
Zahar was a key figure in Hamas' violent takeover of Gaza in 2007, while the other three were members of the Palestinian parliament elected in 2006. Many Hamas leaders have gone into hiding since the beginning of the Israeli offensive.
Alongside the air strikes, Israel also told tens of thousands of residents of the northern town of Beit Lahiya and the Zeitoun and Shijaiyah neighborhoods of Gaza City, all near the border with Israel, to evacuate their homes by 8am Wednesday. The warnings were delivered in automated phone calls, text messages and leaflets dropped from planes.
Palestinian children, who fled their homes close to the border with Israel, unload mattresses at a United Nations-run school in Gaza City. (Reuters photo)
The Israeli military said in its message that large numbers of rockets were launched from these areas and that Israel plans to bomb these locations.
"Whoever disregards these instructions and fails to evacuate immediately, endangers their own lives, as well as those of their families," the message said.
On Wednesday morning, hundreds of residents of Zeitoun and Shijaiyah were seen walking in the streets, carrying small bags with belongings.
HT Edit: A deafening silence from the world as Israel pounds Gaza
Older children carried smaller ones, in their arms or on their backs. Some of the women and children cried, looking terrified.
The Wafa Rehabilitation Center in Shijaiyah, which cares for 15 disabled and elderly patients, received several calls demanding the patients evacuate, said its director, Basman Ashi.
He said an Israel shell hit near the building, causing damage to the second floor, but no injuries. Ashi said he won't evacuate because his elderly patients have nowhere to go.
Israeli soldiers prepare 155mm artillery canons at an army deployment area near Israel's border with the Gaza Strip. (AFP photo)
Four foreign volunteers - from England, the US, France and Sweden - have set up camp at the rehabilitation center to deter the military from targeting it.
English volunteer Rina Andolini, 32, said the patients range in age from 12 to over 70 and none can walk or move without assistance. She said there are also 17 Palestinian staff members.
Andolini said the patients are living in a constant state of fear, intensified by the Israeli tank shelling from across the border.
When asked about the situation at the rehabilitation center, the office of the Israeli military spokesman said its residents "have been asked repeatedly to leave."
"There is a rocket launching site in the area," the military said, adding that Gaza militants use the center to hide "behind civilians."
The military said Iron Dome shot down 23 of the 70 rockets launched at Israel on Wednesday, while the others struck without causing casualties. One salvo, at coastal Ashkelon, forced visiting Norwegian foreign minister Borge Brende into a shelter.
In Gaza's eastern Shejaia and Zeitoun districts, bastions of popular support for Hamas and the Islamic Jihad faction, there was no sign residents were heeding the Israeli call to leave. Authorised by Netanyahu's security cabinet to escalate the offensive, the military relayed warnings to inhabitants in northern Gaza with dropped leaflets and mass phone calls.
"Failure to comply will endanger your lives and the lives of your family," said a recorded message received by residents of Shejaia and Zeitoun, which sprawl out to the barbed-wire border with Israel.
Maher Abu Saa'ed, a 45-year-old doctor in Zeitoun, said that with many areas of Gaza under attack, nowhere was safe and he would not leave despite a telephoned Israeli warning to get out.
"To ask hundreds of people to leave their houses and go to the centre of the city is insane, a sick joke," he said. World powers urged calm, worried about spiralling casualties in one of the world's mostly crowded areas.
Full coverage: Gaza under attack
(With inputs from Reuters, AFP and AP)