Palestinian medical officials say at least 17 civilians, including women and young children, were killed Sunday in Israeli air strikes on the Gaza Strip as Israeli's military ramped up its operation against rocket attacks from the territory.

One of the strikes flattened the two-storey building of the al-Daloo family in Gaza City. Gaza health official Ashraf al-Kidra said four small children from the family and four women are among the dead.

Frantic rescuers pulled the children's bodies from the rubble, including a toddler, as survivors and bystanders screamed in grief. Later, the four children were laid out in the morgue of Gaza City's Shifa Hospital.

It was not immediately clear what the target of the air strike was.

Another aerial bombardment, on a three-storey home in the town of Beit Lahiya, left a three-year-old girl and a five-year-old boy dead. Hamas security officials said three missiles struck the house, owned by a Gaza family with members who are involved in militants' rocket squads. It was not known whether any militants were in or near the house at the time of the strike.

Another strike targeted a Hamas militant in his car outside his home in the Shati refugee camp near Gaza City, but also killed an 11-year-old girl passing by at the time, al-Kidra said.

Israel's Haaretz newspaper reported that the air force attacks had also killed Yehiya Bia, a Hamas member in charge of the group's rocket assaults.

Yet another strike in Gaza City flattened the home of a family known for its support for Hamas, killing three women and a fourth civilian, al-Kidra said.

In total, Sunday's air strikes on Gaza killed nine children ranging in age from one to 11, according to figures provided by al-Kidra.

Al-Kidra said the deaths brought to 70 the number of Palestinians killed in Israel's Gaza offensive, including 36 civilians.

Dozens of rockets fired on Israel

Israel warned earlier Sunday it was widening its range of targets to go after military commanders of the Gaza Strip's Hamas rulers, on the fifth day of its campaign against Gaza rocket operations.

At the same time, Gaza militants continued their barrage of rocket fire, firing more than two dozen at Israel on Sunday, including a longer-distance projectile that targeted Tel Aviv for a fourth straight day. One rocket damaged a home in the southern city of Ashkelon, punching a hole in the ceiling.

"It's been non-stop," Terri Millstone, a Canadian teacher living 50 kilometres south of Tel Aviv in Ashkelon, told CBC News on Sunday.

"Today I've been in [the safe room] a dozen times. I count the booms and then I come out."

Smoke rises after a strike by Israeli forces on Gaza City on Sunday. The Israeli military has widened its range of targets in the Gaza Strip to include the media operations of the Palestinian territory's Hamas rulers. (Bernat Armangue/Associated Press)

Millstone, who does freelance teaching work, says she's worried about her dwindling bank account balance because all of her students have left town along with their families.

"We just want a normal life," she said.

Israel's "Iron Dome" rocket-defence system shot down seven rockets, including the one aimed at Tel Aviv, police spokesman Mickey Rosenfeld said. Eight Israelis were wounded by shrapnel Sunday, one of them moderately, bringing the total number of casualties to nearly 60, including three deaths.

Israeli strikes also hit two media centres in the Gaza Strip on Sunday.

The strikes on the media centres hit two high-rise buildings, damaging the top floor offices of the Hamas TV station, Al Aqsa, and a Lebanese-based broadcaster, Al Quds TV, seen as sympathetic to the Islamists. Six Palestinian journalists were wounded, including one who lost a leg, a Gaza press association said. Foreign broadcasters, including British, German and Italian TV outlets, also had offices in the high-rises.

Lt. Col. Avital Leibovich, an Israeli military spokeswoman, said the strikes targeted Hamas communications equipment on the buildings' rooftops. She accused the group of using journalists as "human shields," and urged journalists to stay clear of Hamas bases and facilities.

Leibovich said the military has identified "hundreds" of additional targets as it pressed forward. She acknowledged that civilians were in danger, but said that Gaza militant groups bore the blame.

"One of the strategies of Hamas... is locating large amounts of munitions underneath civilian homes. Many times this is the reason for this big damage or collateral damage," she said.

Egypt mediates

The repeated militant rocket fire on Tel Aviv and Friday's attack toward Jerusalem have significantly escalated the hostilities by widening the militants' rocket range and putting 3.5 million Israelis, or half the country's population, within reach.

'Israel has every right to expect that it does not have missiles fired into its territory'—U.S. President Barack Obama

Israel finds itself at a crossroads of whether to launch a ground invasion or pursue international-led truce efforts.

Talks brokered by intermediary Egypt took place Sunday. Gaza Prime Minister Ismail Haniyeh of Hamas spoke for for 20 minutes by phone with Egyptian President Mohammed Morsi, Haniyeh's office said.

Haniyeh reportedly told Morsi he supports efforts at a truce, provided Hamas receives "guarantees that will prevent any future aggression" by Israel.

A Palestinian man carries the corpse of a child from the al-Daloo family out from the rubble after an Israeli missile struck the family's home, killing at least seven relatives on Sunday. (Mahmud Hams/AFP/Getty)

An Israeli envoy flew to Cairo for talks with officials there. Israel has said it is not prepared to enter into a ceasefire with Hamas unless it provides guarantees the rocket fire won't resume.

The Arab League, which met in emergency session in Cairo, is sending a delegation to Gaza on Tuesday.

The Egyptian president has also been in touch with leaders from Qatar, Turkey and several Western countries. France's foreign minister, too, is involved and visited Israel on Sunday.

U.S. President Barack Obama, on a three-country trip to Southeast Asia, cautioned Israel against any escalation of its operations even as he backed the Jewish state's right to defend itself. Obama also warned Palestinians the crisis could crush peace hopes for years.

"Israel has every right to expect that it does not have missiles fired into its territory," Obama said.

With files from CBC News