As part of the process, US Secretary of State Condoleezza Rice is expected to visit the Middle East this week and meet separately with Palestinian President Mahmoud Abbas and Prime Minister Olmert.
The Americans expressed their satisfaction with Olmert's dramatic speech in the Negev, during which he turned to the Palestinians and said, "I am coming today from here to offer you to take a different path, a path which offers a chance for a different future for you, as well as for us.
"On Saturday (with the announcement of a ceasefire), we started this path, ad I hope it will lead us to advance toward the objective we all want to achive – peace and quiet and trusting each other."
Olmert also said during his speech that "with the release of Gilad Shalit safe and sound and his return to his family, the Israeli government would be willing to release many Palestinian prisoners, including those sentenced for long period of time."
Officials at the Prime Minister's Office clarified Monday evening that in spite of the government's willingness, "There will be no progress on the issue of the Palestinian prisoners as long as Gilad Shalit does not return. In addition, there is no sensational development on the Shalit issue."
'Obstacles need to be overcome'
US State Department spokesman Sean McCormack welcomed Olmert's speech and defined the ceasefire as "a welcome development, certainly potentially promising."
The American spokesman noted that "Prime Minister Olmert, I think, has through this speech and through his remarks demonstrated that he is truly interested in the dialogue that would lead to a two-state solution, Israel and Palestine living side by side in peace. He has offered up a political horizon to the Palestinians to negotiate in good faith. That's certainly promising.
"But again, before you get to that point, there are obstacles. There are obstacles that need to be overcome," he added.
The American spokesman expressed the United States' willingness to continue to help in promoting a dialogue rather than violence, but detailed the obstacles: "One of them certainly is a Hamas-led government that has not met the Quartet conditions for realizing a political dialogue that eventually leads to a two-state solution.
"Another obstacle are those rejectionist groups who would use violence, who try to derail any sort of hopeful developments or potentially hopeful development."
McCormack expressed his satisfaction over the deployment of the Palestinian forces in the northern Gaza Strip in an effort to halt the Qassam fire. He also knows, however, that the efforts to stop the attacks have not fully succeeded in light of the rockets fired at Israel Monday afternoon.
"It is up to the Palestinian security forces to stop those kinds of attacks," he said.
UN Secretary-General Kofi Annan also welcomed the ceasefire agreement. In his statement, however, he expressed deep concern over the continued firing on rockets at civilian targets inside Israel, saying that these attacks demonstrate the militants' destructive power to sabotage the critical effort to diminish the tension.
Annan also called on both sides to strictly maintain their commitments to broaden the ceasefire also to the West Bank.
Meanwhile, American officials made it clear that Rice's meetings with the Israeli and Palestinian leaders during her upcoming visit to the Middle East have not been scheduled yet.
In light of the ceasefire reached between Israel and the Palestinians, and the visit of Rice and US President George W. Bush to Jordan in the middle of the week, there have been many assumptions that Rice, or maybe even Bush, make hold a joint summit with the Israeli and Palestinian leaders, but sources in Washington noted that the meetings with Abbas and Olmert would probably be held separately.
Attila Somfalvi contrinuted to the report