An Israeli soldier stands near tanks in a deployment area on November 19, 2012 on Israel's border with the Gaza Strip. / Lior Mizrahi/Getty Images
Updated 9:49 p.m. ET
GAZA CITY, Gaza Strip Israel and Gaza's Hamas rulers traded fire and tough cease-fire proposals Monday, and threatened to escalate their border conflict if diplomacy fails. No deal appeared near.
An Israeli airstrike targeting a Gaza media center killed a senior militant and engulfed the building in flames, while Gaza fighters fired 95 rockets at Israel, nearly one-third of them intercepted by an Israeli missile shield. One missile hit an empty school.
A total of 38 Palestinians were killed Monday, 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.
Over the weekend, civilian casualties in Gaza rose sharply after Israel began targeting the homes of what it said were suspected militants. Two such strikes late Monday killed five people - a father and his 4-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 Monday 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."
Israel accuses Hamas militants of hiding near civilians, which Hamas denies. But CBS News correspondent Charlie D'Agata reports the Islamic jihad admitted one of their militants was hiding among journalists when he was killed by an Israeli air strike over the Gaza media center Monday. Launch pads are being discovered near mosques and schools, and CBS News crews saw a rocket launch just two blocks away from a residential area.
Egypt, the traditional mediator between Israel and the Arab world, was at the center of a flurry of diplomatic activity Monday. Egyptian intelligence officials met separately in Cairo with an Israeli envoy and with Khaled Mashaal, the top Hamas leader in exile. Until recently, he has only been allowed in Syria and Iran, CBS News correspondent Clarissa Ward reports.
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 Israel's threat of invading Gaza was a bluff and Hamas would only agree to a cease-fire if its demands are met. "We don't accept Israeli conditions because it is the aggressor," he said. "We want a cease-fire along with meeting our demands."
When asked by Ward if Hamas wants to see a truce, he responded: "God-willing, the American people will wake up and realize that it is better to stand with 350 million Arabs than to continue to support Israel."
Mashaal eventually conceded that he did not want to see an escalation in hostilities, Ward reports, but was unclear on when he thought a truce would be reached. "Perhaps today, perhaps tomorrow, perhaps never," he told reporters.
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.
Still, an Israeli official emphasized that Israel hopes to find a diplomatic solution.
"We prefer the diplomatic solution if it's possible. If we see it's not going to bear fruit, we can escalate," he said, speaking on condition of anonymity because of the diplomatic efforts under way. He added that Israel wants international guarantees that Hamas will not rearm or use Egypt's Sinai region, which abuts Gaza, for militant activity.