International efforts to achieve a cease-fire in the Gaza Strip are approaching the critical point. A senior Israeli official said that U.S. Secretary of State John Kerry has drafted a new cease-fire proposal and presented it to both sides. Kerry, who will leave Cairo Friday afternoon and return to Washington, is awaiting an answer from the Qatari and Turkish foreign ministers as to how Khaled Meshal, the head of Hamas’ political wing, has responded to his proposal.

The Israeli official said that Kerry’s proposal, which he presented to Prime Minister Benjamin Netanyahu at their meeting Wednesday evening, contains the following elements:

1. A one-week, temporary cease-fire, starting Sunday, during which Israel Defense Forces troops will not leave the Gaza Strip entirely and will continue to locate and destroy Hamas tunnels.

2. During this cease-fire, Israel and Hamas will begin negotiations on a more permanent arrangement, with Egyptian mediation. The Palestinian Authority will participate in these talks.

3. The United States, the UN secretary-general and the European Union will provide guarantees to both sides that the negotiations will deal with the issues important to them – for Israel, disarming Gaza of its rockets and tunnels, and for Hamas, ending the blockade of Gaza and repairing the damage the Strip has suffered.

Kerry, who returned to Cairo Thursday night after meeting with Netanyahu, held marathon phone conversations with every international actor who might be able to exert pressure on Hamas, and especially on Meshal, who resides in Doha. Kerry spoke twice with the Qatari foreign minister, Khalid Bin Mohammed al-Attiyah, who is in constant contact with Meshal.

Kerry also spoke with Turkish Foreign Minister Ahmet Davutoglu, who is also in contact with senior Hamas officials; with Egyptian Foreign Minister Sameh Shoukry; and with Jordanian Foreign Minister Nasser Judeh. Kerry also met with UN Secretary-General Ban Ki-moon and spoke by phone with the foreign ministers of Germany, Britain and France and with the European Union’s top foreign policy official, Catherine Ashton, to settle the issue of the international guarantees.

A senior Israeli official said that Kerry will leave Cairo early Friday afternoon, and wants to get an answer from the Qatari foreign minister as to Meshal’s position before he goes. At 1:30 P.M. on Friday, the diplomatic-security cabinet will convene in Tel Aviv to discuss the continuation of the IDF operation in Gaza.

Both Jerusalem and Washington are having trouble predicting how Meshal will respond. The senior Israeli official said that both Hamas officials in Gaza and its delegation in Cairo, which is headed by Moussa Abu Marzouk, support the cease-fire proposal and are unhappy with Meshal’s conduct over the past week.

The official said that either way, Friday’s meeting of the diplomatic-security cabinet is expected to be decisive. If Meshal responds positively to the American proposal, the ministers will vote on a cease-fire in Gaza. If Kerry’s diplomatic efforts fail and Meshal rejects the proposal, the cabinet might well decide to expand the ground operation.

Despite the uncertainty over Meshal’s position, the Hamas leader did signal on Thursday that he is ready to be more flexible. Until then, he had refused to consider any cease-fire before all the issues critical to Hamas, and especially ending the blockade of Gaza, had been resolved. But on Thursday, he said he was ready to halt the fighting in exchange for international guarantees.

On Thursday, British Foreign Secretary Philip Hammond impressed on Netanyahu the need for a swift conclusion to Israel’s ground incursion, although he blamed Hamas for triggering the conflict.

Hammond “stressed the need for a rapid conclusion to [Israel’s] ground operation in Gaza,” and urged that Israeli forces “do everything they can to avoid civilian casualties.”

After his meeting with Netanyahu, Hammond told Sky News of his concern that the world is losing patience with Israel. “As this campaign goes on and the civilian casualties in Gaza mount, Western opinion is becoming more and more concerned and less and less sympathetic to Israel,” he said in the interview. “That’s simply a fact and I have to tell that to my Israeli counterparts.”

Earlier, Netanyahu and Hammond gave a joint press conference at the Knesset, during which Hammond said, “I came to bring this conflict to an end.” He also put the blame on Gaza’s rulers for triggering the current round of fighting.

Netanyahu said, “Hamas and the Islamic Jihad’s use of civilians is extremely cynical. It’s a travesty.”