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The issues, which are key to the peace process, include borders and security, the status of Jerusalem and the return of Palestinian refugees.
Details of these discussions were not revealed.
Talks about core issues for the first time, which did not happen during the first round of talks, are a good indicator, said al-Tahtawy.
Hani Khallaf, Egypt's former assistant foreign minister said that the negotiations being moved to Jerusalem is also a good sign for improvement.
"These negotiations have started in the United States, the international sponsor and then it moved to Egypt, the regional sponsor. Now it moves to Jerusalem. This is a logic development which gives the impression that the Israeli government is serious, " he said.
Khallaf said he believed that peace is achievable within one year as expected by the U.S. administration, who will not accept the wasting of the peace opportunity this time, especially after its vow to improve relations with the Arab and Muslim world.
However, not everything is good for the talks. An Israeli moratorium on the building of settlements in the West Bank, will expire at the end of the month. The tackling of this issue will be a test for the two sides.