Palestinian fighters in Gaza, including Hamas, issued a joint statement on Tuesday announcing an Egyptian-brokered ceasefire with Israel.
The groups said they would abide by the truce as long as Israel did the same, but there was no immediate comment from the Israeli side.
Meanwhile, Kuwait and Bolivia on Tuesday requested an urgent meeting of the UN Security Council to discuss the escalation of violence in the Gaza Strip.
The worst escalation between Israel and Palestinian fighters in Gaza since the 2014 war threatened to plunge the coastal enclave into another full-blown conflict on Tuesday as international mediators raced to pull both sides "back from the brink".
Gaza fighters fired dozens of rockets into southern Israel on Tuesday, killing one person, and Israeli strikes killed two Palestinians as the most serious trading of fire between Israel and militant groups in the enclave for years continued.
Hamas threatened to escalate their rocket attacks if Israel carried out further deadly airstrikes across the coastal enclave. The rulers of Gaza said they would fire rockets at the southern Israeli towns of Beersheba and Ashdod if provoked, a significant threat from the group that has tried to disavow rocket launches emanating from the Strip this year.
A day earlier, renewed violence in Gaza left four Palestinians and one Israeli dead, threatening to put an end to Egyptian and United Nations truce efforts.
Israeli strikes pummelled Gaza, striking more than 100 sites linked to the territory’s rulers Hamas, the military said. They came in response to up to 370 rockets which were fired into Israeli territory in less than 24 hours. Gaza's Health Ministry raised the total Palestinian death toll from violence on Monday and Tuesday to six. Five of those are claimed by Israel to be aligned to Gazan militant groups. At least 25 Palestinians were wounded in the territory in the last 24 hours, the ministry said.
The fierce clashes came after a botched undercover Israeli raid that left one Hamas commander, six fellow fighters and an Israeli officer dead, after the group’s fighters discovered Israeli special forces in a civilian car near the southern Gazan city of Khan Younis.
Israel said it was an intelligence-gathering mission but Hamas vowed revenge for the operation.
A Hamas leader, Ismael Radwan, said the Israeli operation “let the mediators know that the real murder is the Israeli occupation who keep attacking our people". He added that Israel “does not care about the Egyptian efforts”.
The UN, Egypt and the European Union raced on Tuesday to halt the escalation between the two sides.
UN Middle East envoy Nickolay Mladenov called the escalation "extremely dangerous" and said on Twitter that "restraint must be shown by all". He said the UN was working with Egypt to broker an end to the renewed fighting.
Schools were closed in the Gaza Strip and in southern Israel as both sides warned the other that it would respond forcefully to any further violence.
Israeli Prime Minister Benjamin Netanyahu cut short a visit to Paris because of the flare-up, and he returned to Israel on Monday for consultations with security officials.
Michael Oren, a senior Israeli official, said the state “will do whatever it takes” to defend itself. “We expect the world to stand with us,” he said.
The EU’s ambassador to Israel, Emanuele Giaufret, called for a halt in “indiscriminate” rocket fire toward civilians. “Everyone must step back from the brink,” he said.
Late on Monday, an Israeli air strike hit Hamas' Al-Aqsa TV station in the Gaza Strip, forcing it to go off the air. Minutes earlier, it halted its programming. It broadcasted a still image of its logo after the building was hit by a warning missile.
Israeli missile defences intercepted more than 100 rockets from Gaza and most others fell in open areas, though some hit houses and other civilian structures, the military said.
One man was pulled dead from the ruins of a building in southern Israel, emergency services said.
The escalation has come despite Mr Netanyahu's decision to allow Qatar to transfer millions of dollars in aid to the Gaza Strip for salaries as well as fuel to ease an electricity shortage.
The agreements had led to calmer protests along the Gaza border after months of deadly unrest.
Protests along the Gaza-Israel border that began on March 30 have turned deadly, with Israeli snipers opening fire on protesters, many who were unarmed.
Since then, 231 Palestinians have since been killed by Israeli fire, the majority shot during protests and clashes, while others died in tank fire or air strikes.
Two Israeli soldiers have been killed in that time.