Palestinian leaders in Gaza have agreed a ceasefire with Israel, three officials with knowledge of the talks said, after the most serious flare-up since a 2014 war.

Egypt brokered an agreement to cease hostilities, an official from the strip's Islamist rulers Hamas and another from its allied group Islamic Jihad said on condition of anonymity.

An Egyptian official also confirmed the deal on condition of anonymity.

There has been no official confirmation of the ceasefire from Israeli officials.

An AFP correspondent in Gaza said the situation had been calm since the time of the supposed ceasefire. There appeared to have been no Palestinian rocket fire or Israeli airstrikes.

The Islamic Jihad official said the truce agreement was based on Israel easing its blockade of the Gaza Strip.

Among the steps, he said, were the easing of limits on fishing and improvements in Gaza's electricity and fuel situation.

Wissam Zoghbar, an official with the smaller Democratic Front for the Liberation of Palestine in Gaza, said in a statement the deal would see Israel cease all strikes on Gaza.

Earlier, the UN Secretary-General Antonio Guterres had appealed for "maximum restraint" after Israel launched retaliatory strikes in Gaza following rocket fire from the Hamas-controlled territory.

Israel carried out waves of strikes in Gaza on Sunday after Palestinian rockets hit cities in Israel.

Gazan authorities reported at least 23 Palestinians were killed, while Israel said four people were killed in the rocket attacks from Gaza.

"He condemns in the strongest terms the launching of rockets from Gaza into Israel, particularly the targeting of civilian population centers," a UN statement said.

"He urges all parties to exercise maximum restraint, immediately de-escalate and return to the understandings of the past few months," it said.

Mr Guterres's special envoy Nickolay Mladenov was "working closely with Egypt and all concerned to restore calm," the statement said.

Earlier, Israeli Prime Minister Benjamin Netanyahu said he ordered the military to continue "massive strikes" against Gaza's ruling Hamas group and Islamic Jihad, in the most serious border clashes since a spate of fighting in November.

Israel's military said more than 450 rockets, many intercepted by its Iron Dome anti-missile system, have been fired at southern Israeli cities and villages since Friday, and it attacked some 220 targets belonging to Gaza militant groups.

The latest round of violence began two days ago when an Islamic Jihad sniper fired at Israeli troops, wounding two soldiers, according to the Israeli military.

Islamic Jihad accused Israel of delaying implementation of previous understandings brokered by Egypt aimed at ending violence and easing blockaded Gaza's economic hardship.

This time, Israeli strategic affairs analysts said, both Islamic Jihad and Hamas militants appeared to believe they had some leverage to press for concessions from Israel, where independence day celebrations begin on Wednesday.

In two weeks Israel is also hosting the Eurovision Song Contest in Tel Aviv, the target of a Gaza rocket attack in March. That attack caused no damage.

On Sunday sirens sounded in the city of Rehovot, 17 km southeast of Tel Aviv.

In a statement announcing that Israel would press on with its attacks, Mr Netanyahu, who doubles as defence minister, also ordered forces around the Gaza Strip to be "stepped up with tanks, artillery and infantry".

For residents in Gaza, the escalation comes a day before the Muslim holy month of Ramadan begins in the territory on Monday.

It is traditionally a time for prayer, family feasts to break a daylight fast and shopping.

Since Friday, 13 Palestinians of whom five were civilians have been killed in Gaza. They included a 14-month-old baby and the baby's aunt in an air strike, the health ministry said.

Israel's military said its intelligence information showed they were killed by a misfired Palestinian rocket.

Here, Tánaiste Simon Coveney has said he "unequivocally" condemns the rocket attacks from Gaza into Israel over the last two days. 

Minister Coveney said these actions undermined the cause of the Palestinian people.

He said: "The unjust treatment of Gaza and the suffering of people there will never be solved by violence or terrorist attacks."

Mr Coveney called for an end to indiscriminate attacks on civilians and for restraint by Israel’s response, which has already led to several deaths in Gaza.

He said the international community needed to work with all sides to "de-escalate the tension, as a matter of urgency."