In a potentially positive sign, Israeli Prime Minister Benjamin Netanyahu and Palestinian President Mahmoud Abbas planned to hold an extra meeting in this Red Sea resort before shifting to Jerusalem for more negotiations Wednesday, according to Israeli officials who spoke on condition of anonymity because of the sensitivity of the situation.
"The parties have begun a serious discussion on core issues," said President Barack Obama's envoy to the region, George Mitchell, after the leaders met for almost two hours with U.S. Secretary of State Hillary Rodham Clinton, who said the "time is ripe" for a peace deal.
Those issues include determining borders for Israel and a Palestinian state and ensuring security for Israel.
Pressed to say whether there was progress on settlements, Mitchell said, "We continue our efforts to make progress and we believe that we are moving in the right direction, overall."
He repeated Clinton's call for Israel to extend its soon-to-expire curb on settlement construction in the West Bank.
"We think it makes sense to extend the moratorium, especially given that the talks are moving in a constructive direction," he said. "We know this is a politically sensitive issue in Israel. But we've also called on President Abbas to take steps that help encourage and facilitate this process. We believe both sides have a responsibility to help ensure that these talks continue in a constructive manner.
The ultimate aim is a deal that creates a sovereign Palestinian state beside a secure Israel.
The Palestinians want Israel's settlement curb extended beyond the current Sept. 26 deadline. Netanyahu has suggested at least some of the restraints will be lifted.
Clinton said the Obama administration believes Israel should extend the moratorium, but she also said it would take an effort by both sides to find a way around the problem.
"We recognize that an agreement that could be forged between the Israelis and the Palestinians ... that would enable the negotiations to continue is in the best interests of both sides," she said.
Clinton spoke with reporters Monday during a flight from Washington to Egypt for the latest round of talks, which began this month in Washington.
The settlement freeze is not the only wrinkle in the way of launching the talks in earnest. The two sides disagree over what to discuss first: security or borders.
A senior Abbas aide, Mohammed Ishtayeh, appeared to take a hard line on the issue of settlement construction, telling reporters that an Israeli extension of its partial freeze would not signal progress in the negotiations but rather progress in "confidence building."
"The freeze on settlements (construction) is not a topic in the negotiations," he said. "Removing settlements is."
From the Israeli said, Netanyahu spokesman Mark Regev said, "If the expectation is that only Israel has to show flexibility then that is not a prescription for a successful process."
Israeli Interior Minister Eli Yishai, a member of Netanyahu's seven-member inner Cabinet, voiced his opposition to the settlement slowdown, reflecting the intense pressure on the prime minister within his coalition to resume construction once the moratorium ends.
"The freeze in the West Bank is incorrect and its good that it is ending," Yishai told Israel Radio as the meetings in Egypt were taking place.
On Sunday, Netanyahu seemed to reject a total freeze on construction. He said Israel would not build thousands of planned homes. But without providing details or a timeline, he said, "We will not freeze the lives of the residents."
Although some analysts caution that any peace deal faces daunting obstacles, Clinton has said an initial round of talks in Washington on Sept. 2 generated some momentum. They were the first direct in nearly two years.
Associated Press writers Sarah El Deeb and Matti Friedman in Sharm el-Sheikh and Amy Teibel and Diaa Hadid in Jerusalem contributed to this report.