The US Secretary of State Colin Powell held separate talks with the Israeli and Palestinian prime ministers on his latest visit to the region.
Hamas is due to comment on its ceasefire stance again next week
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It used to be the Europeans who did the baby-sitting.
That was the cryptic term used to describe regular visits to persuade Israelis and Palestinians to abandon violence and keep talking to one another.
But on 4 June, at the Aqaba summit in Jordan, President George W Bush indicated Americans were taking direct charge of reviving the peace process.
He pledged that two of his most senior officials, Secretary of State Colin Powell and National Security Adviser Condoleezza Rice, would be personally involved in implementing the Middle East "roadmap".
But almost as soon as the US president had left the region, there was a new and brutal flare-up of violence.
Partial withdrawal
Colin Powell's task is no longer to implement the roadmap but to rescue it.
He has set himself modest goals. He is urging Israel to withdraw from the northern part of the Gaza Strip and the West Bank town of Bethlehem.
And he is urging the Palestinians to take charge of security in these areas.
Mr Powell has been explicit in saying a deal on Gaza and Bethlehem should be finalised regardless of whether the militant Islamic group Hamas agrees to a ceasefire.
Hamas is responsible for many of the suicide bombings in Israeli cities which, time and again, have undermined the prospects for reviving the peace process.
Colin Powell, like the Israeli Government of Ariel Sharon, deeply distrusts Hamas, which he has denounced as an "enemy of peace".
He regards a ceasefire as no more than an interim step towards leading to the eventual disarmament of Hamas and the dismantling of its infrastructure.
Carrot, not stick
Palestinian Prime Minister Mahmoud Abbas, also known as Abu Mazen, is struggling to strengthen his rather shaky personal authority and sees things very differently.
Rather than threatening to crush Hamas, he is offering it the chance to join a new government of national unity - in exchange for renouncing violence.
This shows that, while in principle all the parties are committed to the roadmap, in practice they have sharply differing priorities.
Mr Powell's visit to the region is not over.
He has returned to Jordan for a meeting of the World Economic Forum - the Swiss-based group which brings together politicians, academics, business figures and religious leaders.
Attending the meeting, on the shores of the Dead Sea, will be UN Secretary General Kofi Annan and other senior members of the Quartet - the US, the UN, Russia and the European Union.
It was the Quartet which produced the roadmap last year, and its members will want to discuss its current rather fragile state of health.