Hamas called for a 24-hour ceasefire in Gaza ahead of a major Muslim holiday after Israel resumed its military operations.
A spokesman for the Palestinian group said the truce would be in effect from 2pm (12pm BST) in the lead-up to Eid al-Fitr, which caps the fasting month of Ramadan.
It came after Hamas rejected Israel's offer late on Saturday of a 24-hour extension to a 12-hour humanitarian ceasefire which was respected by both sides.
More rockets were fired towards Israel, prompting the Israeli Defence Forces (IDF) to restart operations.
Lt Col Peter Lerner, an Israeli army spokesman, did not confirm whether the IDF would hold fire following the new truce requested by Hamas, but said that troops would carry on demolishing Hamas military tunnels.
Labour former deputy prime minister John Prescott today added his voice to those criticising Israel's bombardment of Gaza, which he described as "brutally disproportionate and grossly indiscriminate".
Lord Prescott said any other country would be made an international "pariah" if it acted in the same way.
And he directly compared the situation in Gaza with a concentration camp, suggesting the Nazi Holocaust should "give Israelis a unique sense of perspective and empathy with the victims of a ghetto".
"Imagine a country claiming the lives of nearly three times as many as were lost in the MH17 plane tragedy in less than three weeks," Lord Prescott wrote in the Sunday Mirror.
"A nation which blasted a hospital, shelled and killed children from a gunboat as they played football on the beach and was responsible for 1,000 deaths, at least 165 of them children, in just two weeks.
"Surely it would be branded a pariah state, condemned by the United Nations, the US and the UK. The calls for regime change would be deafening.
"But these howls of protest are muted. The condemnation softened. For this is Israel."
Thousands of pro-Palestinian demonstrators marched through London yesterday, many of them branding Israel a "terror state".
Foreign Secretary Philip Hammond, speaking after crisis talks with US Secretary of State John Kerry and other foreign ministers in Paris yesterday, urged both sides to extend the cessation of violence in a bid to stem the loss of life.
"The necessity right now is to stop the loss of life and you stop the loss of life by getting this ceasefire to roll over for 12 hours, or 24 hours or 48 hours, and then again and again," he said.
Israel's latest campaign in the Gaza Strip, which began on July 8, has killed more than 1,050 Palestinians, mainly civilians, according to Palestinian health officials.
Israel has lost 43 soldiers, while two Israeli civilians and a Thai worker have been killed by rocket and mortar attacks from Gaza.
More than 2,400 rockets have been fired toward most of Israel's major cities, but casualties have remained low due to the Iron Dome aerial defence system.
Eid al-Fitr, one of the most important holidays in the Muslim calendar, is expected to begin on Monday or Tuesday, depending on the sighting of the new moon.
The IDF claimed Hamas had continued to launch rockets against Israel after their ceasefire began.
The military force tweeted: " The Iron Dome just intercepted 4 rockets over Beersheba. Hamas continues to fire at Israel from Gaza."
The IDF released a statement denying it was responsible for the deaths of some 15 women, children and UN workers at a UN Relief and Works Agency (UNRWA) school in northern Gaza on Thursday.
A spokesman said that the Israeli military force had conducted a "comprehensive inquiry regarding the incident" in Beit Hanoun.
It claimed to have found that a "single errant mortar" hit the school's courtyard when it was "completely empty", despite multiple reports that the premises had been crowded with people seeking shelter.
"The inquiry concluded that during the intense fighting between IDF forces and Hamas militants, the militants operated adjacent to the UNRWA school," the spokesman said.
"The militants fired anti-tank missiles at IDF soldiers, who then responded by firing several mortars in their direction," the army statement said.
"The inquiry... concluded that a single errant mortar landed in the courtyard of the UNRWA school, when it was completely empty.
"The IDF stresses it does not operate or target international organisations in the Gaza Strip, and the ongoing coordination conducted via the Coordinator of Government Activities in the Territories (COGAT) is continuous without change, even during times of combat.
"In light of the inquiry's findings, the IDF rejects the claims that were made by various officials immediately following the incident, that people were killed in the school premises as a result of IDF operational activity."
It came after former prime minister Gordon Brown decried the bombing or damage to a total of 120 schools - more than 70 run by UNRWA - since the military campaign began in Gaza.
Writing in the Observer, Mr Brown said: "As the UN secretary general, Ban Ki-moon, has said, schools are for learning and must never become theatres of war.
"They should be safe havens for boys and girls, and their violation is a crime against international law.
"And whatever the provocation, their militarisation - by whatever means - should be outlawed."
US President Barack Obama stressed in a call to Israeli Prime Minister Benjamin Netanyahu his "serious and growing concern" about the number of Palestinian civilian deaths and the loss of Israeli lives, as well as the worsening humanitarian situation in Gaza.
Mr Obama also stressed the need for an "immediate, unconditional humanitarian ceasefire" to end hostilities.
And he called for the disarmament of terrorist groups and the demilitarisation of Gaza in order to end the Israeli-Palestinian conflict.