On the face of it, the situation on the ground in the Middle East in the wake of last week's terrorist attacks in New York and Washington could scarcely look bleaker. Radical Palestinians and other Arabs have been filmed celebrating the carnage. Israel has stepped up its attacks on towns and villages in the West Bank, with 20 Palestinians killed in the past week. The polarisation appears complete.

Yet it is precisely at such a grim time that the opportunity should be grasped to revive the peace process. The US is seeking to build the widest possible international coalition in support of its war on terrorism. To succeed, President George W. Bush needs the backing of as many moderate Middle East leaders as possible. But if the conflict in Israel continues to escalate, his whole strategy could be undermined.

That is why the US administration is urging both sides to return to talk again. The message has not been lost on Yassir Arafat, the Palestinian leader. His public donation of blood for victims of the New York atrocity was a determined effort to counter the negative images of Palestinian celebrations. Shimon Peres, the Israeli foreign minister, is keen to reopen talks. But Ariel Sharon, the prime minister, shows no sign of compromise. He is now demanding 48 hours of "complete quiet" as a precondition for talks on a ceasefire. That sounds like stalling.

Of course it is tempting for the Israeli security forces to exploit the international horror at the terrorism in America. The Palestinians are in disarray, and many Americans would applaud every tough Israeli move. But an escalation of the conflict is precisely what the hijackers wanted to gain the greatest possible sympathy in the Arab world for their cause. Israel's hard-line response is inflaming the situation.

The violence must be calmed. Clearly that means an end to Palestinian suicide attacks, as well as to Israeli reprisals. It is not certain that Mr Arafat can control the most militant factions on his side. But last week's terrorist onslaught appears to have persuaded him, and other Arab leaders, that they must line up with the US in its determined response. That may well not be popular with their own people. But their good faith should be put to the test.

Mr Sharon is also being asked to go against his public opinion. A large majority in Israel believes the peace process is finished. But there is just a chance that the terrible bloodshed in America could prove a catalyst for change. The Arabs are putting pressure on Mr Arafat for restraint. This is not the time for Mr Sharon to be stepping up the conflict.