An Israeli airstrike targeting a Gaza media centre killed a senior militant and engulfed the building in flames.
Gaza fighters fired 95 rockets at southern Israeli cities, nearly one-third of them intercepted by an Israeli missile shield.
A total of 38 Palestinians were killed yesterday, bringing the death toll since the start of Israel's offensive to 111, including 56 civilians.
Some 840 people have been wounded, including 225 children, Gaza heath officials said. Three Israeli civilians have been killed and dozens have been wounded.
Two such strikes last night killed five people -- a father and his four-year-old twin sons in northern Gaza and two people in the south, medics said.
Jamal Daloo, who lost his wife, a son, four grandchildren and five other members of his family in an attack Sunday, sat in quiet mourning next to the ruins of his home, his face streaked with tears.
"The international public opinion witnessed the facts," he said, speaking as his 16-year-old daughter, Yara, was still missing under the rubble being cleared away by bulldozers. "This does not require my words."
The Israeli military says Gaza militants fire rockets from residential areas. Last night it released footage it said showed what was a militant weapons depot hidden in a Gaza neighbourhood.
Egypt, the traditional mediator between Israel and the Arab world, was at the centre of a flurry of diplomatic activity yesterday. Egyptian intelligence officials met separately in Cairo with an Israeli envoy and with Khaled Mashaal, the top Hamas leader in exile. Hamas wants Israel to halt all attacks on Gaza and lift tight restrictions on trade and movement in and out of the territory that have been in place since Hamas seized Gaza by force in 2007. Israel demands an end to rocket fire from Gaza and a halt to weapons smuggling into Gaza through tunnels under the border with Egypt.
With positions far apart on a comprehensive deal, some close to the negotiations suggested Egypt is first seeking a halt to fighting before other conditions are discussed. They spoke on condition of anonymity because the talks are in a sensitive stage.
Mashaal told reporters that Hamas would only agree to a ceasefire if its demands are met. "We don't accept Israeli conditions because it is the aggressor," he said. "We want a ceasefire along with meeting our demands."
Mashaal also suggested that Israel's threat of invading Gaza was simply a ploy. He said Israeli Prime Minister Benjamin Netanyahu "is waving the threat of a ground offensive and asking the world to pressure Egypt, Turkey and Qatar, so they pressure Hamas".
"He wants to negotiate with us under fire to impose his conditions, pretending he is acting from a position of strength," Mashaal said.
Israeli leaders have repeatedly threatened to widen the offensive, saying an invasion is an option. Israel has amassed troops on the Gaza border and begun calling up thousands of reservists.
An Israeli official said: "We prefer the diplomatic solution. If we see it's not going to bear fruit, we can escalate," he said. He added Israel wants international guarantees Hamas will not rearm or use Egypt's Sinai region, which abuts Gaza, for militant activity.