GAZA CITY, Gaza Strip – Israel rejected mounting international pressure to suspend its air offensive against Gaza militants whose rocket barrages are striking close to the country’s heartland, sending warplanes Wednesday to demolish the smuggling tunnels that are Islamic Hamas’ lifeline.

The diplomatic action has been set in motion by the scale of destruction in Gaza since Israel unleashed its campaign on Saturday and a death toll that Gaza officials now put at 374. Hamas says some 200 uniformed Hamas security forces have been killed and the United Nation says at least 60 civilians have died. Four Israelis have been killed by militant rocket fire, including three civilians.

Overnight, Prime Minister Ehud Olmert discussed a 48-hour truce proposal floated by France with his foreign and defense ministers. The meeting ended with a decision to pursue the punishing aerial campaign, defense and political officials said. They spoke on condition of anonymity because the discussion’s contents were classified.

“Giving Hamas a respite just to regroup, rearm is a mistake,” Olmert spokesman Mark Regev said. “The pressure on the Hamas military machine must continue.”

Calls for an immediate cease-fire have also come from the United States, the European Union, the U.N. and Russia.

President Bush and Secretary of State Condoleezza Rice personally called leaders in the Middle East on Tuesday to press for a durable solution.

The moderate Palestinian president, Mahmoud Abbas, is set to meet later Wednesday with Turkey’s prime minister, Recep Tayyip Erdogan, in Jordan to discuss a possible cease-fire. Abbas will also meet with Jordan’s King Abdullah II. Both Jordan and Turkey have mediated in the past between Israel and its enemies.

Underlying the Israeli decision to keep fighting are the mightier weapons that Hamas has smuggled into Gaza through underground tunnels along the border with Egypt. If previously militants relied on crude homemade rockets that could fly just 12 miles to terrorize Israeli border communities. Now they are firing industrial-grade weapons that have dramatically expanded their range and put more than one-tenth of Israel’s population in their sights.

More than two dozens rockets and mortar shells were fired inti Israel by mid-day Wednesday, including five that hit in and around the major southern Israeli city of Beersheba, 22 miles from Gaza. One hit an empty school. Another landed in a small farming community about 20 miles southeast of Tel Aviv. No serious casualties were reported.

School was canceled in large swaths of Israel’s south because of the rocket threat. The 18,000 students at Ben-Gurion University in Beersheba, southern Israel’s only university, were also told to stay home.

Early on Wednesday, Israeli aircraft pounded smuggling tunnels under the Gaza-Egypt border in another attempt to sever the lifeline that keeps Hamas in power by supplying weapons, food and fuel. Israel and Egypt blockaded Gaza after Hamas violently seized control of the territory in June 2007, and have cracked open their borders only to let in limited amounts of humanitarian aid.

A huge explosion rocked a tunnel that housed a fuel pipeline. In all, two tunnels were destroyed in the raid, Egyptian security officials in Rafah said.

An Egyptian official, speaking on condition of anonymity because he wasn’t authorized to speak to the media, said Israel has destroyed 120 tunnels since the aerial campaign began. According to conservative estimates, there were at least 200 tunnels before Israeli warplanes began striking.

In Gaza City, powerful airstrikes sent high-rise apartment buildings swaying and showered streets with broken glass and pulverized concrete. The Israeli military said government buildings were hit, including an office of Gaza’s Hamas prime minister, Ismail Haniyeh.

A Palestinian medic was killed and two others were wounded when an Israeli missile struck next to their ambulance east of Gaza City, Palestinians said. The Israeli military said it did not know of the incident.

Israeli navy ships also fired at Hamas positions along the coastline.

Israel has been massing troops and armor along the Gaza border in an indication the air campaign could morph into a ground operation. The government approved a plan to call up an additional 2,500 reserve soldiers late Tuesday, following a decision earlier this week to authorize a call-up of 6,700 soldiers. The call-ups have yet to be carried out.

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

While rejecting the truce, Israel said it would allow 2,000 tons of food and medical supplies to enter Gaza on Wednesday, in addition to 4,000 tons the military says have been allowed in since the offensive began. Several dozen chronically ill Gazans have also been authorized to enter Israel for treatment Wednesday, the military said.

The U.N. planned to resume food aid distribution on Thursday, after halting it two weeks ago because of shortages caused by the blockade. Most of Gaza’s 1.4 million residents rely on U.N. food handouts.

Foreign Minister Tzipi Livni was to travel Thursday to Paris for talks with French President Nicolas Sarkozy, who has put his growing international stature to use in other conflict zones, most recently to help halt fighting between Russia and Georgia in August.

Kouchner said Wednesday he and Sarkozy are considering traveling to Israel next week.

A Hamas spokesman said militants wouldn’t halt their rocket and mortar fire until Israel ended its blockade. “If they halt the aggression and the blockade, then Hamas will study these suggestions,” Mushir Masri said.

Israel fears that opening crossings with Gaza would allow Hamas — which remains officially committed to Israel’s destruction — to strengthen its hold on the territory even further.

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Associated Press Writer Matti Friedman reported from Jerusalem and Sarah El Deeb reported from Cairo.