Conscious of the worldwide implications of failure, yet deeply pessimistic about their prospects of success, UN Secretary-General Mr Kofi Annan, US President Bill Clinton and Egypt's President Hosni Mubarak will today hold summit talks with Israel's Prime Minister, Mr Ehud Barak, and the Palestinian Authority President, Mr Yasser Arafat.
The summit comes amid a relative fall-off in West Bank and Gaza violence, but also amid news of a dramatic widening of the conflict - with the pro-Iranian Hizbullah movement yesterday announcing it had captured a senior Israeli army officer.
Israel said the man was a colonel in the reserves who was kidnapped on a private business trip to Europe. It denied he was a Mossad operative.
After 18 days of violence in which about 100 people, almost all of them Palestinians, have been killed, Mr Barak and Mr Arafat are now so mistrustful of each other that, as of last night, they had still not consented to meet face to face at the talks, which are to be hosted by Mr Mubarak at the Egyptian port of Sharm al-Sheikh. Instead, a complicated series of bilateral meetings is envisaged, at which the two leaders will meet in turn with the various wouldbe mediators, including Jordan's King Abdullah and possibly Russian President Vladimir Putin.
Mr Annan noted that the entire international community was watching and that "global economic growth" was at stake.
And yet the very best that all parties reasonably expect from the summit is a denunciation of violence and a ceasefire agreement.
For Mr Arafat, even attending the talks has meant defying calls from the Palestinian street for an end to negotiation and an escalation of the so-called "Al-Aksa Intifada" - the uprising named for the mosque atop Jerusalem's Temple Mount. And for Mr Barak the summit comes amid his own disillusion with Mr Arafat as a peace partner, and with a new crisis developing over the capture of the Israeli officer.
Israel, at the summit, intends to press for the rearrest of dozens of Islamic militants freed by the Palestinians in recent days, a halt to shooting by Palestinian police and militia, and an end to what it calls anti-Israeli incitement in the Palestinian media.
The Palestinians are demanding that Israel end its military blockade around West Bank cities, and that an international inquiry be held into the violence.