Israel may halt its air strikes in the Gaza Strip for 48 hours if Hamas also stops sending rockets into border towns. But the ceasefire proposal, put forward by French officials, is still being weighed by the Israeli government.

News of the possible ceasefire came as Israel conducted air assaults against Hamas targets for a fourth day. So far, a reported 375 Palestinians have been killed and upwards of 1,400 injured in the densely-populated area, while four Israelis have died.

A Hamas spokesperson told The Associated Press that it would be willing to end its rocket attacks, but only if Israel also ceased its blockade of the Gaza Strip. Residents have little access to medical supplies, food and fuel.

"If they halt the aggression and the blockade, then Hamas will study these suggestions," said Mushir Masri.

The current crisis began roughly a week after a six-month truce between Israel and Hamas ended with a barrage of Hamas rocket fire. On Christmas day, 80 rockets were fired from Gaza into southern Israel.

"Unfortunately this is not a fight that Israel sought. It's a fight we sought to avoid. But it was forced upon us and we are responding," Israeli government spokesperson Mark Regev told Canada AM.

"I think Hamas is being taught now a lesson and it's a difficult lesson, it's a hard lesson for them," he added. "But they have to learn if they shoot at Israeli civilians they will pay a price, and hopefully in the future they will be a bit more careful about what they do."

While Hamas appears to have been shocked by the robust campaign, the militant organization is also regrouping and managing to strike back with rockets, including some long-range missiles.

"Zionists, wait for more from the resistance," Hamas spokesman Ismail Radwan said in a text message to reporters, referring to militants' armed struggle against Israel.

Diana Buttu, a former legal advisor for the Palestinian Liberation Organization, told CTV Newsnet she was skeptical about the truce having much of an impact on the blockade.

"Even if they do halt their assault on the Gaza Strip, it's not entirely clear they're going to allow medical supplies in," she said by phone from Ramallah, in the West Bank.

"They haven't allowed such supplies in for a very long period of time, and food and medical supplies are dwindling as we speak."

She said that the Fatah government in the West Bank is united with Hamas in the Gaza Strip over Israel's military actions, and both have called for international intervention.

Buttu also doubted Israel would stop its campaign if Hamas ended its rocket attacks.

"I think what will bring this to a resolution is if we get international intervention," she said. "The rules of the game have to be following international law, rather than this simple 'might is right.' When you follow that strategy of 'might is right,' all that it demonstrates is that violence is the only solution. I personally don't believe that."

Hamas targets

Israeli aircraft on Tuesday blasted a Hamas government complex, security installations and the home of a top militant commander.

Meanwhile, thousands of troops were being amassed on the border along with tanks and artillery, ready to go in on the ground -- the likely next step in the escalating conflict.

Most of the Palestinian casualties were security forces, but at least 64 were civilians, according to the United Nations.

The Israeli deaths included three civilians and one soldier.

Mackey Frayer suggested there is no easy solution in sight for the conflict.

"Neither side seems to be backing down here and nobody really wants to talk about a ceasefire," she said, noting that Barak has been spreading the message on U.S. talk shows that asking Hamas for a ceasefire would be akin to the U.S. asking al Qaeda for a ceasefire.

Israeli politicians are also maintaining that past ceasefires have only been of benefit to Hamas, giving the group the opportunity to re-arm and regroup for more attacks, Mackey Frayer said.