They have agreed to develop a framework for a permanent peace deal during talks held in Washington, and also to meet for direct talks every two weeks in the region.[break]
US Secretary of State Hilary Clinton has said core issues between the Israelis and Palestinians could be resolved within one year.
"If you move forward in good faith and do not waiver in your commitment to succeed on behalf of your people, we can resolve all of the core issues within one year," Mrs Clinton said.
The two sides will next meet at the Egyptian resort of Sharm el-Sheik on September 14 and 15 and there will be other meetings also involving the US and other members of the Quartet.
Israeli Prime Minister Benjamin Netanyahu said: "Just as you expect us to be ready to recognise a Palestinian state as the nation state of the Palestinian people, we expect you to be prepared to recognise Israel as the nation state of the Jewish people".
Following an attack earlier in the week in which four Israeli settlers were shot dead in a random attack, Palestinian leader Abbas acknowledged Israeli concerns over security, but also called for action from the Israelis.
"Once again, we want to state our commitment to follow on all our engagements, including security and ending incitement, and we call on the Israeli government to move forward with its commitment to end all settlement activities and completely lift the embargo over the Gaza Strip and end all form of incitement," he said.
Council on Foreign Relations´ Robert Danin,said: ""There may be some room there for creative diplomacy to try to bridge those two positions.
"If so, then it would be a very important sign of progress and show that the United States is able to finesse difficult issues. It will build a level of trust and optimism between the two sides".
Beyond this first challenge, the two sides will be working to agree on how they will pursue peace.
"The purpose of a framework agreement will be to establish the fundamental compromises necessary to enable them to flesh out and complete a comprehensive treaty that will end the conflict and establish a lasting peace between Israel and the Palestinians," US Middle East envoy George Mitchell said.
All the core issues are on the table though - like the status of Jerusalem, settlements, security and refugees.
Representatives of Hamas the group which controls Gaza, came out to denounce the talks, vowing to continue attacking Israelis.
Prime Minister Netanyahu indicated that broader regional tensions also needed to be considered.
"..and we´ve had the rise of Iran and its proxies and the rise of missile warfare. And so, a peace agreement must take into account security arrangement against these real threats that have been directed against my country," he said.
The US makes it clear that it cannot force a settlement and that the course of peace is dependant on the ability of the two sides to make the necessary painful concessions.
But no one, it seems, is under any illusion of the difficulty and complexity of the task ahead.
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