Five Palestinians died on Sunday in surging cross-border fighting while Israel alleged that rockets from Gaza killed three people in an Israeli city.

In Gaza, at least four Palestinians were killed in Israeli strikes, health officials said.

In a separate strike it described as a targeted attack, Israel's military killed Hamed Ahmed Al Khodary, a Hamas commander. The military said he was responsible for transferring funds from Iran to armed factions in Gaza.

The air strike on his car was the first such killing of a top militant since the war five years ago. Israel had suspended such attacks in a bid to lower tensions.

The sounds of sirens and explosions reverberated on both sides of the frontier, fraying nerves and keeping schools closed.

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.

On Saturday four Palestinians including a baby, her mother and a youth died in Israeli airstrikes on Gaza on Saturday. Cross-border hostilities which broke out on Friday flared into a second day, with Gazans fleeing Israeli strikes and air-raid sirens sending Israelis running to shelters as interceptor missiles blew up Palestinian rockets in the sky.

The escalation of the conflict, which comes just ahead of the Holy month of Ramadan prompted Israeli Prime Minister Benjamin Netanyahu to convene a high-level meeting of his security chiefs.

Explosions shook Gaza City, where busy streets were packed with shoppers carrying out their Ramadan preparations.

The Gaza Health Ministry said a 14-month old baby and her mother were killed by one of the Israeli strikes and at least 12 other Palestinians were wounded. Residents identified two of them as fighters.

“The Israeli plane fired a missile near the house and the shrapnel entered the house and hit the poor baby,” said her aunt.

Smoke rises following an Israeli air strike in Gaza City on Monday. Suhaib Salem/Reuters

Islamic Jihad said in a statement that the rocket barrages were a response to Friday’s events and that Israel has been delaying the implementation of previous Ibtessam Abu Arar. An Israeli military spokeswoman made no immediate comment. A small armed pro-Hamas group in Gaza, the Protectors of Al Aqsa, said one of its men was killed in another air strike.

Egyptian mediators, credited with brokering ceasefires in previous rounds of violence, were working to prevent further escalation of hostilities.

The latest round of violence began on Friday when a Palestinian Islamic Jihad sniper fired at Israeli troops, wounding two, according to the Israeli military.

Israel retaliated with an air strike that killed two Palestinians from the Hamas group, which controls Gaza. Two other Palestinians protesting near the frontier were killed by Israeli forces on the same day, Palestinian officials said.

Hamas and Islamic Jihad began firing waves of rockets into Israel early on Saturday. The Israeli military said its tanks and aircraft responded with strikes against more than 30 targets belonging to both groups.

Israeli military spokesman Lieutenant-Colonel Jonathan Conricus said Israel was prepared to intensify its attacks. He added that Islamic Jihad was trying to destabilise the border and blamed Hamas for failing to rein it in.

Islamic Jihad said in a statement that the rocket barrages were a response to Friday›s events and that Israel has been delaying the implementation of previous understandings brokered by Cairo.

In a joint statement, Hamas and Islamic Jihad said: “Our response will be broader and more painful if the enemy pursues its aggression.”

The European Union on Saturday called for rocket fire from Gaza into Israel to “stop immediately” and threw its backing behind efforts by Egypt and the UN to calm the situation.

“The rocket fire from Gaza towards Israel must stop immediately. A de-escalation of this dangerous situation is urgently needed to ensure that civilians’ lives are protected,” EU spokeswoman Maja Kocijancic said in a statement.

“Israelis and Palestinians both have the right to live in peace, security and dignity.”

Hamas said on Thursday that its Gaza chief, Yeyha Sinwar, had travelled to Cairo for talks on efforts to maintain calm along the border and alleviate hardship in the enclave.

“Egypt has stepped up its efforts with Hamas, the Islamic Jihad and Israel, but there is no conclusion yet,” said a Palestinian official familiar with Cairo’s mediation efforts.

The United Nations has also been part of the Cairo talks. Although aerial exchanges are a frequent occurrence, Israel and Hamas have managed to avert all-out war for the past five years.

Israel, whose Prime Minister Netanyahu won a fifth term in office on April 9, is due to host the 2019 Eurovision song contest finals in less than two weeks in Tel Aviv, towards which long-range rockets were launched in mid-March.

Some 2 million Palestinians live in Gaza, whose economy has suffered years of blockades as well as recent foreign aid cuts. Unemployment stands at 52 per cent, according to the World Bank, and poverty is rampant.

Smoke rises following an Israeli air strike in Gaza City on Sunday. Suhaib Salem/Reuters

Israel says its blockade is necessary to stop weapons reaching Hamas, with which it has fought three wars since the group seized control of Gaza in 2007.

Over the past few weeks, Cairo›s mediation had helped persuade Israel to lift some restrictions on the movement of goods and people in and out of Gaza and expand the Mediterranean zone where Gazans can fish.

But Israel scaled back the fishing zone this week in response to rocket fire and shut the border crossings entirely on Saturday after barrages from Gaza.

Agencies