Smoke rises following an explosion on the Gaza side of the Israel-Gaza border as it is seen from its Israeli side. Picture: Amir Cohen/Reuters

Gaza/Jerusalem - Rockets and missiles from Gaza killed three civilians in Israel while Israeli strikes killed 12 Palestinians, most of them militants, in surging cross-border fighting on Sunday, according to Gazan officials and the Israeli military.

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 600 rockets and other projectiles - over 150 of them intercepted by its Iron Dome anti-missile system - have been fired at southern Israeli cities and villages since Friday.

It said it attacked more than 260 targets belonging to Gaza militant groups. Gaza officials said Israeli air strikes and artillery fire killed 20 people including eight civilians since Friday.

A rocket that hit a house in Ashkelon on Sunday killed a 58-year-old man, police said. He was the first such Israeli civilian fatality since the seven-week-long Gaza war in 2014.

Another rocket strike in Ashkelon killed a factory worker, a hospital official said. The military said a third civilian was killed by an anti-tank missile fired at his car from Gaza near the border.

In Gaza, Islamic Jihad identified seven fighters killed in Israeli strikes, while medical officials said three civilians also died.

In what it said was a separate, 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. Hamas confirmed Khodary had been killed.

The attack on his car was the first such killing by Israel of a top militant since the war five years ago. Israel had suspended what Palestinians call an assassination policy 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.

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 (10.5 miles) southeast of Tel Aviv.

In a statement announcing that Israel would press on with its attacks, 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 Ramadaan begins in the territory on Monday. It is traditionally a time for prayer, family feasts to break a daylight fast and shopping.

Among the eight Gazan civilians killed since Friday were a 14-month-old baby and the baby's aunt, according to the health ministry. Israel's military said the intelligence information showed they were killed by a misfired Palestinian rocket.

In Gaza, two Palestinian human rights groups described the cause of their deaths as an explosion whose source was still undetermined.

A U.N. envoy said it was working with Egypt to try to end the fighting. Iran condemned what it called Israel's "savage" attack on Gaza, and blamed "unlimited U.S. support" for Israel.

Israeli bombings in Gaza destroyed two multi-storey structures. Witnesses said the Israeli military had warned people inside to evacuate the buildings, which it alleged housed Hamas security facilities, before they were hit.

Saeed Al-Nakhala, owner of a clothing store in one of the buildings, said he had had no time to save his merchandise.

"I was together with my son in the shop, there was a big noise and then another and people started to run. We left everything behind and escaped," said Nakhala.

Some 2 million Palestinians live in Gaza, whose economy has suffered years of Israeli and Egyptian blockades as well as recent foreign aid cuts and sanctions by the Palestinian Authority, Hamas's West Bank-based rival.

Unemployment in Gaza stands at 52 percent, according to the World Bank, and poverty is rampant.

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, two years after Israel withdrew its settlers and troops from the area.

Reuters