Israeli Prime Minister Benjamin Netanyahu vowed on Sunday to continue "massive strikes" in response to rocket fire from the Gaza Strip as a deadly escalation entered a second day, sparking fears of wider violence.

Gazan authorities reported six Palestinians killed, including at least two militants, by Israeli strikes in the latest round of fighting that began on Saturday as militants fired hundreds of rockets into Israel.

But Israel disputed their account of the deaths of a pregnant mother and her baby, blaming errant Hamas fire.

One 58-year-old Israeli man was killed overnight by a rocket strike on the city of Ashkelon near the Gaza border, Israeli police and medics said.

"I instructed the [military] this morning to continue its massive strikes on terror elements in the Gaza Strip," Netanyahu said at the start of a cabinet meeting.

He said he had also ordered "tanks, artillery and infantry forces" to reinforce troops already deployed near Gaza.

The flare-up came as Hamas, the Islamist movement that rules the blockaded enclave, sought further concessions from Israel under a fragile months-old ceasefire.

Israel said its strikes were in response to Hamas and Islamic Jihad firing 450 rockets or mortars across the border since Saturday, with Israeli air defences intercepting more than 150.

'Immediately de-escalate'

In addition to the Israeli man killed, an 80-year-old woman was seriously injured in a rocket strike on the Israeli city of Kiryat Gat, police and medics said.

A man was also hospitalised in Ashkelon, said police, citing other injuries without providing details.

A house near Ashkelon was damaged and other rockets hit open areas.

The Israeli army said its tanks and planes hit some 220 militant targets in Gaza in response. They included an Islamic Jihad attack tunnel that stretched from southern Gaza into Israeli territory, it added.

Two multi-storey buildings in Gaza City were also destroyed.

Israel said one of the buildings included Hamas military intelligence and security offices.

Turkey said its state news agency Anadolu had an office in the building, and strongly denounced the strike.

Israel said the other building housed Hamas and Islamic Jihad offices.

The Gaza health ministry said Israeli strikes killed a 14-month-old baby and her pregnant mother, 37, as well as four Palestinian men.

But Israeli army spokesperson Jonathan Conricus said that based on intelligence "we are now confident" that the deaths of the mother and baby were not due to an Israeli strike.

"Their unfortunate death was not a result of [Israeli] weaponry but a Hamas rocket that was fired and exploded not where it was supposed to," he said.

Islamic Jihad identified two of the dead men as its militants. The ministry said 47 other people were wounded.

Hamas ally Islamic Jihad claimed responsibility on Saturday for at least some of the rocket fire and said it was prepared for more.

Its armed wing distributed a video showing militants handling rockets and threatening key Israeli sites, including Ben-Gurion international airport near Tel Aviv.

Israel closed its crossings with Gaza for people and goods, as well the fishing zone off the enclave's shore, until further notice.

Egyptian and UN officials held talks to calm the situation, as they have done repeatedly in the past, while the European Union called for an immediate halt to rocket fire from Gaza.

The UN envoy for the Israeli-Palestinian conflict, Nickolay Mladenov, called on "all parties to immediately de-escalate and return to the understandings of the past few months".

The United States condemned Gaza militants and said it fully supported Israel's "right to self-defence against these abhorrent attacks".

Jordan, one of only two Arab countries with a peace treaty with Israel, urged it to "end its aggression against the Gaza Strip and respect international humanitarian law".

Visit to Cairo

The escalation follows Friday clashes along the Gaza border that were the most violent in weeks.

Four Palestinians, including two Hamas militants, were killed after two Israeli soldiers were wounded in a shooting during weekly protests on the frontier.

Israel and Gazan militants have fought three wars since 2008 and fears remain of a fourth.

A ceasefire between Israel and Hamas, brokered by Egypt and the United Nations, had led to relative calm around Israel's April 9 general election.

But recent days saw an uptick in violence, placing the ceasefire at risk.

A Hamas delegation led by its Gaza head Yahya Sinwar visited Cairo on Thursday for talks with Egyptian officials.

The truce has seen Israel allow Qatar to provide millions of dollars in aid to Gaza, paying salaries and financing fuel purchases to ease severe electricity shortages.

Israel has several reasons to seek calm.

Netanyahu is engaged in tough negotiations to form a new government following April's election.

Israel is also due to host the high-profile Eurovision song contest in Tel Aviv from May 14-18, expected to attract thousands of spectators.

The country celebrates its Independence Day on Thursday.

Muslims in Gaza will mark the start of the Islamic holy month of Ramadan in the coming days.