In late July, when Barack Obama toured the Middle East, he met the Palestinian president, Mahmoud Abbas, for a private briefing on the state of the world's most intractable conflict - a major priority for the next occupant of the Oval Office.

Abbas revealed later that when he told the Democratic candidate about the Arab peace initiative - offering Israel normal relations with all 22 Arab countries in exchange for a Palestinian state - Obama's (clearly private) response was unambiguous: "The Israelis must be crazy not to accept that."

It's a telling anecdote that is highly relevant as Arabs and Israelis await the outcome of the US election and ponder how - or whether - their faltering peace process can be sustained or revived once a new administration is in place. After eight disastrous years of George Bush, and zero hopes for an 11th-hour negotiating breakthrough between Palestinians and Israelis, there is a real thirst for change in Washington.

And it is also high time, some argue, to revisit that Arab initiative not because it can by itself resolve those knotty bilateral issues of borders, settlements, Jerusalem and refugees - but because it could help persuade sceptical Israelis that there are benefits and a place for them in the wider Middle East.

The plan Abbas described to Obama was launched by the Saudi Crown Prince (now King) Abdullah at the 2002 Beirut Arab summit, and it is another leading Saudi royal who is promoting it again now: Prince Turki al-Faisal, the king's nephew, is the ex-head of Saudi intelligence as well as former ambassador to London and Washington. Not much has happened in the Middle East in the last 30 years that he wasn't involved in or doesn't have intimate knowledge of.

So despite insisting that he was speaking as a private individual, there was rapt attention this week when he appealed to Israelis to listen carefully to what the initiative actually says - and to respond positively to it.

Every Arab state, as Turki put it, "made clear that they will pay the price for peace, not only by recognising Israel as a legitimate state in the area, but also to normalise relations with it and end the state of hostilities that had existed since 1948."

The quid pro quo was that Israel too must "accept peace as a strategic choice ... withdraw completely from all the lands they occupied in 1967, including Jerusalem ... accept a just solution for the refugee problem ... and recognise the independent state of Palestine."

No serving Israeli officials were present at the "track-two" dialogue organised by the Oxford Research Group. But former (and still influential) denizens of the worlds of diplomacy, the military and intelligence were there along with a leading pro-Abbas Palestinian, senior Egyptians, Americans and Britons. Representatives of Hamas, Syria and Iran, either official or unofficial, were conspicuously absent.

It was common ground that part of the problem is that the Arab initiative was overshadowed by the worst incident of the second intifada - when a Palestinian suicide bomber killed 30 Israelis at their Passover meal on the eve of the Beirut summit - and Israel reoccupied most of the West Bank.

The plan generated headlines when it was re-endorsed, again under Saudi auspices, at the Riyadh Arab summit last year. But thanks to Israeli objections it did not get a mention when Bush convened the Annapolis conference a few months later. The Annapolis goal of Israeli-Palestinian agreement by the end of his presidency looks like a bad joke.

Ignorance is part of the problem. As someone quipped: you can wake an Israeli of a certain age at 3am, say the word "Khartoum" and he will immediately identify the post-1967 war Arab summit in the Sudanese capital that produced three notorious "noes" - no peace, no recognition, no negotiations with Israel (which set the Arab consensus, broken only by Egypt, for the next 20 years). But the Saudi plan, which says exactly the opposite, is still likely to produce blank stares at any time.

Ehud Olmert, Israel's outgoing prime minister, misrepresented the Arab initiative as a take-it-or-leave-it diktat, claiming it required the return of millions of Palestinian refugees - a red line for the any Israeli government - when it in fact talks sensibly of reaching "a just solution". Nor does it preclude negotiating land swaps, for example, so that Palestinians would get territory to compensate them for areas where post-1967 Israeli settlements cannot be moved.

Israelis who are familiar with the plan often say they still crave some grand gesture as evidence of Arab goodwill - citing Anwar Sadat's dramatic, taboo-breaking journey to Jerusalem in 1977 (though in fact Sadat had been promised the return of the Sinai peninsula before he got on the plane).

The response, from Prince Turki and others, is that Arab relations with Israel cannot undergo wholesale "normalisation" - a highly sensitive word in the political lexicon of the Middle East - until Israel shows it is prepared to resolve the Palestinian issue. Settlement activity in the West Bank - doubled since Oslo in 1993 and continuing since Annapolis - is hardly a signal of that.

"Instead of talking about whether the glass is half full or half empty," said one participant, "I prefer to say there is bucket with some water in it but holes about one third of the way up: the holes are the settlements and whatever progress has been made we can't make any more until those holes are plugged."

So it is good news that leading Israelis are planning a campaign to breathe new life into the Arab peace initiative, advertising the benefits of a comprehensive settlement which consigns the entire conflict to history. Polling shows Israelis no longer believe in Oslo-like incrementalism with a distant goal held hostage to endless process. Improved salesmanship can certainly popularise a good but neglected product.

But there will have to be substantial change if there is to be anything for the next US president to work with. "The Israelis need to show the Arabs that they are prepared to pay a political price to move forward - and that it's not all about tactics," warned a senior Arab diplomat. "No amount of PR will work until there is a meaningful peace process that has some chance of going somewhere."