After pounding Hamas in Gaza for four days, senior Israeli defense officials are considering a 48-hour truce to see whether Hamas will halt its rocket attacks in return, Israeli defense sources told ABC News.
The possibility of a truce is expected to be discussed at Israel's security Cabinet meeting Wednesday.
The impetus behind the suggestion by "senior voices within the IDF," the Israeli Defense Force, is to see how Hamas responds, Israeli sources told ABC News. If Hamas rejects the truce and continues to fire rockets at Israeli cities and towns, Israel would have more legitimacy to press ahead with its offensive, including a possible ground invasion into the Palestinian enclave.
An escalation of Israel's military operation to include the use of ground forces is what many third parties are trying to avoid. The devastation would prove too costly for both sides, experts say. Hamas has 15,000 well armed men, trained to fight Israeli forces in the alleyways of Gaza.
"It means tanks – it means soldiers. It means fighting Hamas face to face in many places – in Gaza," Israeli defense analyst Ronnie Sheked said.
The cease-fire proposal hasn't been formalized or accepted by Israeli Prime Minister Ehud Olmert, but experts say a long-term cease fire is in Israel's interest. In return for a cease-fire, Hamas will likely demand open border crossings and more supplies.
President Bush spoke with Palestinian Authority leader Mahmoud Abbas and Egyptian President Mubarak today, urging them to press Hamas militants to enter into a sustainable truce. Abbas' regime governs the West Bank but has no control over the Gaza Strip. The United States has no diplomatic ties to Hamas, which it has designated a terrorist organization.
A National Security Council spokesman said the purpose of the president's conversations was to lead to a "sustainable and lasting" cease-fire.
The possibility of a cease-fire emerged as the Israelis and Hamas fighters continued to trade blows for a fourth day, and the death toll rose to more than 375 dead and more than 1,400 injured.
The United Nations reports at least 50 of those killed were civilians, but the director of a Gaza Strip hospital told ABC News the civilian death count stands at more then 120, including 21 children.
On the ground, there is no sign of a truce. Earlier today, witnesses told The Associated Press that Israeli aircraft had dropped at least 16 bombs on five Hamas government buildings in a Gaza City complex, destroying them, igniting fires and sending rubble flying hundreds of yards away.
One Israeli officer told ABC News that after this operation is over, not one building belonging to Hamas in Gaza will be left standing.
Israeli forces are also going after Hamas rockets. The launch zones from where the rockets attack Israeli cities like Sderot, the warehouses where the rockets are stored, loaded and transported, all are being obliterated.
Recent reports claim that as much as 50 percent of Hamas rockets in Gaza have been destroyed.
Nevertheless, Hamas continues to launch rocket attacks into Israel, despite the all-out assault against the group by Israeli aircraft. A medium-range rocket reached 26 miles to the city of Beersheba -- farther than ever before -- slamming into an empty kindergarten. Israeli forces say they successfully struck the group that launched the rocket.
Overnight, two Israelis were killed by Hamas rockets, bringing the total number of Israelis killed to four since Saturday.
The Bush administration spoke out Monday on the Israeli assault of Hamas targets throughout Gaza, condemning Hamas for the escalation of violence.
"In order for the violence to stop, Hamas must stop firing rockets into Israel and agree to respect a sustainable and durable cease-fire," White House spokesman Gordon Johndroe said Monday. "That is the objective to which all parties need to be working. That is what the United States is working towards."
Israeli Foreign Minister Tzipi Livni told ABC News that "Hamas represents an extreme Islamic ideology. They are not fighting for Palestinian rights. They are to deny us our right to exist."
In Gaza, conditions have worsened for its 1.5 million residents. The territory's nine hospitals report they are overwhelmed by the wounded. Palestinian residents are digging through the rubble to find and free survivors. On Gaza's southern border, Egypt shut its crossing after thousands of Gazans tried to escape the fighting and breached the border wall.
Netanyahu Says Hamas 'Will Have to Go'
The human cost of the Israeli bombing of Gaza is enormous. Among the hundreds killed are five sisters, age 4 to 17. They were crushed to death Monday when a wall collapsed in their home after an Israeli airstrike.
One of the surviving sisters spoke to ABC News: "We were sleeping. We woke up and we were buried in the rubble. My 4-year-old sister sleeping next to me died."
Two more young sisters, aged 4 and 11, were killed today in another Israeli strike in northern Gaza.
At Gaza's biggest hospital, Shifa, the injured keep pouring in with each new airstrike. Since Saturday, the hospital has treated more than 200 people with traumatic injuries, even though its intensive care unit is designed to serve just 25.
Medical supplies in the hard-hit Gaza enclave are few and food stocks are rapidly being depleted. Shifa's Dr. Kamal Abada told ABC News that they are running especially low on essentials like bandages, sutures and critical medicine.
Saturday night the hospital itself was hit. Shifa workers collected the injured from their own parking lot. Since the hospital's glass windows were shattered in the attacks, the nights are so cold that attendants cover the windows with plastic sheeting.
Dr. Rawea Awad is now a patient, after she suffered a massive head injury on her way to the hospital. Abada admitted that he and his colleagues are afraid to come to work, but he said they are more afraid to stay home.
Israel has allowed some supplies in, offering hope for medical aid and generators to reach the hospital. The Israeli Defense Force said today it opened the gates for 110 trucks of medicine, food, cooking oil, sugar and flour.
In addition, Egypt opened its Rafah crossing to allow 30 to 35 trucks filled with tents, blankets and medical supplies for those who had lost their homes, according to the Red Crescent charity. Most of the aid that came through Rafah was provided by Qatar, Saudi Arabia, Libya, and Egypt.
But if there is an Israeli ground offensive the level of human suffering is expected to grow much worse with both sides having to engage in fierce urban fighting.
Speaking at a special session of parliament Monday, Ehud Barak, Israel's defense minister, said the country is engaged in a "war to the bitter end" against Hamas in Gaza but declined to give details of how far that war would go to stop Hamas rocket attacks.
Barak is a candidate in Israel's election. Former Prime Minister Benjamin Netanyahu, the current front-runner, hinted at a broader campaign to end Hamas' rule in Gaza.
Netanyahu told Reuters today that a government under his leadership would use "all means necessary" to end Hamas' rule in Gaza.
And in an interview with Fox News, he said that to truly eliminate the threat of rocket attacks Hamas "will have to go." Ending the threat once and for all "will entail bringing down the Hamas regime sooner or later," he said. Israeli elections are scheduled for Feb. 10.
Israeli tanks remain poised on the Gaza border, waiting for the call. At this point, there seems to be no end in sight to the Israeli operation.
ABC News' Martha Raddatz and the Associated Press contributed to the reporting of this story.