It is unclear how calm can be achieved
Israel has said it is halting all offensive operations against the Palestinians, following the ceasefire call from Yasser Arafat, the Palestinian leader.
But can the violence of the last year in which more than 700 people have been killed now be brought to a halt?
Commentators are now wondering if those who carried out last week's attacks against the United States may, unwittingly, have achieved what months of international diplomacy have failed to bring about - real progress towards a genuine ceasefire in the Middle East.
The shock of events in New York and Washington have certainly concentrated both Israeli and Palestinian minds.
Difficult position
Suddenly there is a new international priority - President Bush's war against terrorism - and both Yasser Arafat and the Israeli Prime Minister, Ariel Sharon, are eager to show their support for it.
This is much harder for Mr Arafat than it is for Mr Sharon.
For one thing, there can be no guarantee that his men will carry out his increasingly insistent demands for a full ceasefire.
For another, he will now be expected by both the Israelis and the Americans to crack down on the Islamist groups who in the past have carried out suicide bombings and who have bitterly opposed any ceasefire.
Past mistake
But the Palestinian leader finds himself in a weak position.
Above all, he is anxious to avoid making the mistake he made a decade ago after Iraq's invasion of Kuwait when he alienated both the Americans and the Saudis by showing sympathy for the Iraqi leader Saddam Hussein.
This time he wants to be on the winning side, even if that means running certain risks with Palestinian public opinion.
Risks
In the short run, it will not be easy to achieve the 48 hours of calm which Mr Sharon is demanding.
That in turn is supposed to lead to a further seven days of quiet.
Only then will the two sides be able to discuss implementing the Mitchell plan - the peace proposals put forward earlier in the year by the former American senator George Mitchell.
There will be risks at every turn.