Jerusalem (CNN) -- The Elders, an independent group of leaders brought together by former South African President Nelson Mandela to promote Mideast peace, travel to Israel on Thursday.
On Tuesday, the group -- including former U.S. President Jimmy Carter-- met in Syria with the exiled leader of Hamas, the Palestinian movement that runs Gaza.
Carter, former Irish President Mary Robinson, former U.N. envoy Lakhdar Brahimi, and Ela Bhatt, founder of the million-strong Self Employed Women's Association of India, were the four "Elders" who met with Hamas' Khaled Meshaal.
The group's Middle East tour has taken them to Gaza and Egypt. It is expected to visit the West Bank as well.
The Elders said in a statement that talks with a range of people in Gaza, Egypt and Syria led them to back a "more comprehensive approach to the Israeli-Palestinian peace talks."
The Elders have repeatedly heard that there are low expectations that the current U.S.-led talks between Israel and the Palestinian Authority will succeed.
"A far greater sense of urgency is needed. People are tired after almost two decades of talks," Robinson said. "They keep telling us that there is too much focus on process and not enough on results. They are asking themselves whether the United States and the Quartet are more interested in managing the conflict than resolving it. As Elders, we believe the two-state solution has the potential to deliver peace -- but a more energetic and comprehensive approach is needed."
The Quartet is made up of the United Nations, the United States, the European Union and Russia, which has backed the so-called road map to a Middle East peace.