The UN Security Council held an emergency meeting on Sunday after Israel's devastating new attack on a Lebanese village but the United States again blocked any condemnation of its ally in a special statement.
France meanwhile pushed for a separate full resolution calling for an immediate halt to fighting between Israel and Hezbollah which has left hundreds dead.
The 15-member council met at the request of UN Secretary General Kofi Annan and Lebanese Prime Minister Fuad Siniora after the Israeli raid on the southern Lebanon village of Qana left about 52 people dead, including at least 30 children.
"We must condemn this action in the strongest possible terms, and I appeal to you to do likewise," Annan told the council.
"I'm deeply dismayed that my earlier calls for immediate cessation of hostilities were not heard, with the result that innocent lives continue to be taken and innocent civilians continue to suffer," he said.
Annan criticised Israel and Hezbollah. "It is important to stress that both sides in this conflict bear a heavy responsibility, and there is strong prima facie evidence that both have committed grave breaches of international humanitarian law."
But the council was unable to agree a statement that was demanded by Qatar which wanted a call for a cessation of hostilities to be included and called the Israeli attack a deliberate act.
Diplomats said US ambassador John Bolton again led opposition to the strong wording in the statement. But he said he still hoped that a compromise could be reached on Sunday.
"I think what we're going to try to do today is see if we can agree on a presidential statement or a press statement that will express our profound regrets and condolences to the families of those who have died" in Qana, he said.
The United States also refused to allow a condemnation of Israel in a statement released after the killing of four UN peacekeepers in Lebanon on Tuesday.
France has circulated its proposed resolution calling for a halt to fighting to other Security Council members but there has been no formal debate.
The draft "calls for an immediate cessation of hostilities" and "emphasizes the need to create the conditions for a permanent ceasefire and a lasting solution to the current crisis between Israel and Lebanon."
According to the draft, a permanent ceasefire and resolution to the crisis would involve "the release of the abducted Israeli soldiers and the settlement of the issue of the Lebanese prisoners detained in Israel."
It would also require "full implementation" of previous UN resolutions, "including the disarmament of all militias in Lebanon and the extension of the government of Lebanon's authority over all its territory."
France's resolution calls for the establishment of a buffer zone which would be free of any armed personnel and equipment "other than those of the Lebanese armed and security forces and of UN mandated international forces."
President George W. Bush sidestepped calls for an immediate ceasefire between Israel and Hezbollah, but vowed Sunday to work with the United Nations for what he called "a sustainable peace" in the region.
"The United States is resolved to work with members of the United Nations Security Council to develop a resolution that will enable the region to have a sustainable peace, a peace that lasts," Bush told reporters in Washington.
The US ambassador to the United Nations, said: "Obviously we want to move urgently to try and find a way to reach that solution which will help create an enduring cessation of hostilities in the region," he said.
Before the Security Council even met on Sunday, Israeli Prime Minister Ehud Olmert told US Secretary of State Condoleezza Rice that Israel needs another 10 to 14 days to complete its offensive in Lebanon, according to an Israeli official.