Israel continued its aerial bombardment of Hamas targets in the Gaza Strip Tuesday, as international pressure for a ceasefire mounted and Israeli officials warned operations against the militant group were only just beginning.

Israel continued its aerial bombardment of Hamas targets in the Gaza Strip Tuesday, as international pressure for a ceasefire mounted and Israeli officials warned operations against the militant group were only just beginning.

European foreign ministers met Tuesday in Paris, calling for an end to hostilities and increased access to Gaza for humanitarian purposes. An Israeli government official said French President Nicolas Sarkozy is planning to come to Israel on Monday to try and broker a ceasefire.

Turkey's prime minister, meanwhile, announced a round of shuttle diplomacy to Arab capitals to consult on a response to the attacks. The Israeli aerial bombardment, which began Saturday, has now claimed at least 350 Palestinians, including 60 civilians, according to United Nations estimates Tuesday.

Israel's security cabinet meets Wednesday to discuss the military operation, and Israeli press reports late Tuesday suggested a possible ceasefire would be on the agenda. The military denied an earlier report that it had recommended a 48-hour ceasefire, and a government spokesman said he had no knowledge of plans to discuss a halt to the operation during Wednesday's meeting.

Militants inside the enclave kept up a barrage of attacks Tuesday into southern Israel and vowed to send rockets further into the country. Gaza-launched rockets have killed four Israelis, including one soldier, so far. Late Tuesday, a Hamas missile hit the Israeli desert town of Bersheba, expanding the known range of its arsenal.

Despite mounting international pressure for a return to a six-month ceasefire between the two sides - which ended two weeks ago - Israeli government spokespeople maintained throughout the day that the time wasn't ripe for talk of renewing the pact.

"An instant fix that doesn't solve anything isn't a solution. We'll be back in a month or two months in a round of violence like today," said Mark Regev, a spokesman for Prime Minister Ehud Olmert. "You need to create a situation in which Hamas understands that it isn't in their interest to shoot at innocent Israeli civilians."

Mr. Olmert shrugged off concern growing in Washington and European capitals about a prolonged war, telling his nation that the operation was still in its initial stages.

With infantry and armored units massing at the Gaza border, Israel's air force launched 40 strikes in the Gaza Strip on Tuesday. Israeli officials said they had targeted administrative buildings used by Hamas government officials, police stations, border tunnels and weapons store houses.

Inside Gaza, eyewitnesses reported a GazaCity sports club, two mosques, and the homes of several Hamas militants were also targeted.

At ShifaHospital, the Gaza Strip's largest, doctors struggled with shortages of staff and supplies to provide care for the injured. In the 12-bed intensive care unit doctors are now tending to 53 critically injured patients, said Haitham Dababish, the hospital's emergency room director.

"Our medical teams are exhausted and our sources of medical supplies are running out," Dr. Dababish said. "If we continue like this the whole system will collapse."

Meanwhile, Palestinian militants lobbed at least 40 missiles into southern Israeli towns. Hamas has vowed it won't surrender and has promised to continue missile strikes as well as renew a campaign of suicide attacks.

Hamas spokesman Fawzi Barhoum, one of the few Hamas leaders not in hiding, urged Palestinians to respond to Israel's military operation with "all available means."

The Gaza fighting, the worst in decades, has risked instability spilling over into other countries in the region. Thousands have demonstrated in Arab capitals, criticizing leaders for acting too cautiously to halt the attacks.

Egyptian President Hosni Mubarak, who has angered Arabs across the region for refusing to open that country's border with Gaza, said Tuesday the crossing would remain largely shut until the Palestinian Authority regained control over Gaza. (Hamas won Palestinian-wide elections in 2006 and then forcefully took control of Gaza in 2007.) Egypt allowed a trickle of wounded Palestinians across the border Monday.