For the first time in almost a year, the guns truly fell silent for much of yesterday, as the Palestinian and Israeli leaderships moved determinedly to enforce their ceasefire. But isolated Palestinian gunfire at Jewish homes in the divided West Bank city of Hebron, and a response from Israeli troops, punctured the quiet yesterday evening. Palestinian officials reported one man killed and five injured.
And later last night, two dozen grenades were fired at an Israeli army position in southern Gaza.
Islamic extremist groups in the West Bank and Gaza Strip vowed to defy the truce - announced by the Palestinian Authority President, Mr Yasser Arafat, on Monday, and matched by the Israeli Prime Minister, Mr Ariel Sharon, on Tuesday - and to continue "resist ance of all kinds", presumably including suicide bombings.
But Mr Arafat, who is calling for US intervention to maintain the ceasefire, has plainly followed through on his pledge to give directives to his loyalists to hold their fire, and Mr Sharon has moved Israeli tanks and other forces out of the Palestinian territory in which they were encamped outside Jenin and Jericho. Aides to Mr Arafat are now calling for Israel to ease the restrictions on movement between Palestinian cities in the West Bank.
The European Union's foreign policy chief, Mr Javier Solana, says that Israeli and Palestinian security chiefs may meet as soon as today to try and re-establish some kind of working partnership, and an oft-cancelled meeting between Mr Arafat and the Israeli Foreign Minister, Mr Shimon Peres, may be imminent too. Mr Sharon had demanded "48 hours of quiet" before such talks could take place; that demand, which had seemed thoroughly improbable, now appears almost realistic.
The Bush Administration is expressing tentative relief at the changed atmosphere here. Having pressed hard on both sides, behind the scenes, for a truce, President Bush said late on Tuesday that he now discerned "a glimmer of hope" and mused that perhaps the September 11th terror attacks in the US might at least have prompted something productive in the Middle East. "I hope in my heart of hearts that out of this evil comes good," he said.
While Mr Arafat spent yesterday shuttling between Egypt and Jordan for talks with President Mubarak and King Abdullah, he has real problems to confront at home. His security forces were out demonstratively yesterday in Rafah, at the south of the Gaza Strip, which has been a daily flashpoint for Israeli-Palestinian friction. But thwarting the Islamic extremists' threat will require far more than a show of force.
Mr Arafat has always publicly maintained that Islamic extremists are acting in defiance of his wishes when orchestrating suicide bombings, but Mr Sharon is adamant that this is not the case. If any Palestinian groups carry out attacks on Israel, whether or not Mr Arafat condemns them, said aides to Mr Sharon yesterday, that would constitute a breach of the ceasefire.
AFP adds: President Bush yesterday urged Mr Arafat to back up a condemnation of terrorism "with action" and said he felt "a sense of optimism" about progress towards Middle East peace.
"Would that Chairman Arafat backs up his strong statement with action. We take his words very seriously," he said.
Last week's terror strikes on New York and Washington "may shake up the attitudes of the Middle East where people would end up resolving to show the world that there could be peace there as well. And progress is being made," said Bush.