She was due for more three-way talks on Wednesday with Israeli Prime Minister Benjamin Netanyahu and Palestinian president Mahmud Abbas, a day after two lengthy sessions with the two leaders in Egypt's resort of Sharm el-Sheikh.

On her first visit to the Middle East since launching new direct peace talks in Washington on September 2, Clinton discussed the partial 10-month Israeli freeze on settlements due to expire this month, US officials said.

US envoy George Mitchell, who participated in the talks in Egypt, said the Israeli and Palestinian leaders "began a serious discussion on core issues."

These are Israel's security, the borders of a future Palestinian state, the fate of Palestinian refugees and the future of Jerusalem, but he did not identify the subjects discussed.

In remarks after Clinton boarded the plane for Israel, a senior US official hailed what he called "the seriousness and sincerity of the leaders to reach an agreement, to resolve these issues."

He characterised their talks as "direct," but also "polite."

In Egypt, Mitchell gave no tangible sign of progress when reporters asked if the two sides had taken steps toward reconciling Palestinian demands for a halt to the settlements and pressure in Israel to continue them.

He repeated President Barack Obama's remarks on Friday that it "made sense" to extend the 10-month partial moratorium in the West Bank and recalled appeals to Abbas to "take steps that help encourage and facilitate this process."

When pressed on whether progress had been made on settlements, Mitchell replied: "We continue our efforts to make progress and we believe that we are moving in the right direction overall."

On her flight Monday to the Middle East, Clinton did not rule out a deal between the two sides that would result in something short of an extension of the partial freeze, which is due to expire at the end of this month.

The Palestinians have warned that if the moratorium is not extended, the talks could come to a complete halt.

Egyptian foreign ministry spokesman Hossam Zaki backed the Palestinian position.

"No one should expect Egypt to convince the Palestinians of what they are not convinced of; they have a clear position on this issue and we support them," he said.

But Zaki played down talk of deadlock.

"It's too early, let's see what transpires. It is naive to think that something concrete would come out of only the second round of talks."

A senior member of Abbas's Fatah party, Hatem Abdel Qadir, told Egyptian television on Monday that Washington was pressuring the Palestinians to drop their condition of a complete settlement freeze for the talks to continue.

But a member of the negotiating team, Nabil Shaath, said after Clinton met Abbas that the Palestinian leader was not asked to reverse his condition on settlements.

Tuesday's talks were also expected to tackle the agenda for the negotiations, with Netanyahu reportedly wanting first to address future security arrangements and secure Palestinian recognition of Israel as a Jewish state.

But the Palestinians want first to define the borders of a future Palestinian state, address the status of Jerusalem and discuss the right of return of refugees who fled or were driven out of what is now Israel in 1948.

Netanyahu spokesman Mark Regev said Israel was seeking to negotiate an agreement quickly but one that would be implemented over a long period.

During the flight, Clinton also said the "time was ripe" for a solution to the conflict.

"If you listen to both leaders, they recognise time is not on either of their sides," she said.

Besides the talks in Jerusalem on Wednesday with Netanyahu and Abbas, Clinton is also due to meet Israeli President Shimon Peres and Foreign Minister Avigdor Lieberman.

She will also meet Palestinian prime minister Salam Fayyad.

Mitchell meanwhile was due to hold talks with Syrian President Bashar al-Assad in Damascus on Thursday, the US embassy there said.

US officials attending the peace talks said Mitchell would then travel to Lebanon for talks with top officials.

A senior US official told reporters on condition of anonymity that Mitchell would look at ways to revive Syria's talks with Israel as he searches for a comprehensive Middle East peace with all of the Jewish state's neighbours.

And Israeli public television said Netanyahu is considering travelling to Washington on Sunday for talks with senior US officials.

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