UNITED NATIONS — A cease-fire initiative Tuesday to halt the increasingly bloody Israeli offensive in Hamas-rule Gaza won support from Palestinian President Mahmoud Abbas. Secretary of State Condoleezza Rice called on rival sides to follow up on the proposal.

Egyptian President Hosni Mubarak said the initiative seeks an immediate cease-fire by Israel and Palestinian factions for a specific period to allow secure corridors for delivery of humanitarian aid into Gaza and give Egypt time to continue efforts to reach a permanent cease-fire.

Egypt is inviting the warring Israeli and Palestinian sides for urgent meetings to resolve issues underlying the fighting, including securing Gaza's borders, reopening all crossings and lifting the Israeli "siege," Mubarak said.

The U.N. Security Council held a high-level emergency meeting late Tuesday as international pressure mounted for an end to the 11-day Israeli offensive in Gaza that has killed nearly 600 Palestinians, about half of them civilians, and injured at least 2,500, according to U.N. and Palestinian officials.

Israel says it launched the air and ground attack to end Hamas rocketing that has traumatized southern Israel. Hamas, a militant Islamic group which the U.S. and Israel consider a terrorist organization, wrested control of Gaza from the Palestinian Authority in June 2007.

At Tuesday's four hour council meeting, virtually every Arab speaker denounced the Security Council's failure to adopt a legally binding resolution to stop the Israeli offensive and demand a durable cease-fire.

Saudi Foreign Minister Prince Saud al-Faisal said the council's "deafening silence" placed "a big question mark" over its credibility "and the entire system of international security."

Arab League Secretary-General Amr Moussa said the Egyptian and French presidents launched their initiative, which the league's 22 members support, because of the council's procrastination.

"We do not see any contradiction between that initiative and the work of the Security Council," he said. "In fact, they both complement each other ... since our objective is the same."

To try to spur speedy council action, Libya formally circulated a revised Arab draft resolution Tuesday that, in party, calls for a cease-fire, the withdrawal of Israeli forces and the opening of all crossings into Gaza.

But the draft makes no mention of a key U.S. and Israeli demand — for border monitors to destroy tunnels that Hamas has used to smuggle arms since seizing control of Gaza. In fact, it never mentions Hamas by name.

The Security Council scheduled another meeting Wednesday morning.