GAZA CITY, Gaza Strip - Israel, under international pressure, is considering a 48-hour halt to its punishing four-day air campaign on Hamas targets in Gaza to see whether Palestinian extremists will stop their rocket attacks on southern Israel, Israeli officials said yesterday.

Any offer would be coupled with a threat to send in ground troops if the rocket fire continued.

Prime Minister Ehud Olmert discussed the proposal - floated by France's foreign minister - and other possible next steps with his foreign and defense ministers, Israeli officials said, speaking on condition of anonymity.

President Bush and Secretary of State Condoleezza Rice called leaders in the Middle East to press for a durable solution beyond any immediate truce.

And members of the Quartet of world powers trying to promote Mideast peace - the United States, United Nations, European Union and Russia - concluded a conference call with an appeal for an immediate cease-fire.

The EU itself late yesterday also urged an immediate truce and called on Israel to reopen borders to allow vital supplies to reach Gazans. A statement by the 27-member bloc avoided blaming either side for the current fighting.

Israel's leadership trio, in its meeting last night, stepped up preparations for a ground offensive, surveying cabinet ministers by phone on a plan to call up an additional 2,500 reserve soldiers, if required. Earlier this week, the cabinet authorized a call-up of 6,700 soldiers.

After the four-hour meeting, Olmert's office said in a statement early today that no details of the discussion would be made public because of the sensitivity of the subject matter.

But Israeli officials, speaking on condition of anonymity, said the leaders wanted Hamas to agree to stop the rocket fire before Israel considers a truce.

And even amid talk of a truce, Israeli warplanes unloaded more bombs on targets in Gaza. Powerful air strikes caused Gaza City's high-rise apartment buildings to sway and showered streets with broken glass and pulverized concrete. Israel's ground forces on Gaza's border also used artillery for the first time.

Hamas kept up its rocket barrages, which have killed four Israelis since the weekend and sent many more running for bomb shelters.

A medium-range rocket hit Beersheba for the first time ever, zooming 28 miles deep into Israel and slamming into an empty kindergarten. A second rocket landed in an open area near the desert city. The military said later that it successfully struck the group that launched those rockets.

Four days into a campaign that has killed 374 Palestinians and prompted Arab and international condemnation, the diplomatic push to end the fighting gathered pace.

In two calls to Defense Minister Ehud Barak, Monday and yesterday, French Foreign Minister Bernard Kouchner appealed to him to consider a truce to allow time for humanitarian relief supplies to enter the Gaza Strip, two senior officials in Barak's office said.

Foreign Minister Tzipi Livni was expected to travel tomorrow to Paris for talks with French President Nicolas Sarkozy, who has put his growing international stature to use in other conflict zones.

Israeli media reported that Sarkozy would also travel to Jerusalem on Monday for talks with the Israeli and Palestinian leaders.

Hamas spokesman Mushir Masri said any halt to extremist rocket and mortar fire would require an end to Israel's crippling blockade of Gaza. "If they halt the aggression and the blockade, then Hamas will study these suggestions," Masri said.

Any cease-fire would face questions about its long-term viability. In the past, Hamas has been unable or unwilling to rein in all the extremists, some of whom belong to different factions.

Israel's military said it hit 31 targets yesterday, including a cabinet building, rocket-launching sites, and missile-building sites. It kept up air attacks early today.

A spokesman for Hamas' military wing, Abu Obeida, said Hamas remained strong and vowed to fight on as long as Israel continued its air strikes.

And if there is a ground invasion, Obeida promised worse: "If you enter Gaza, the children will collect your flesh and the remains of your tanks, which will be spread out through the streets."

Egypt, which has been blockading Gaza from its southern end, has come under pressure from the rest of the Arab world to reopen its border with the territory because of the Israeli campaign. But Egyptian President Hosni Mubarak said yesterday that his country would not do so unless Palestinian Authority President Mahmoud Abbas - a rival of Hamas - regained control of the border post.

Mubarak has been rattled by the presence of a neighboring Islamic ministate in Gaza, fearing it would fuel more Islamic dissidence in Egypt.