Take a couple of dozen Nobel prize winners, an Arab monarch and a famous Jewish writer and Holocaust survivor. Put them in a beautiful setting, ply them with fine food and magnificent hospitality, organise brainstorming sessions - and you get a memorable opportunity to chew over some of the gravest problems on the planet.

Petra, the Nabataean city "half as old as time," is the rose-red jewel in the crown of Jordan's heritage sites - and one of the wonders of the world. It also hosts an annual conference of Nobel laureates launched by King Abdullah and Elie Wiesel: the big issues being discussed this week included the global food and energy crises, economic development, scientific research and youth empowerment – a hot topic in a region where half the population is under 18.

Woven into the clubby atmosphere, civilised discussion and endless networking possibilities is the theme of Arab-Jewish and Jordanian-Israeli cooperation - one of the fruits of the peace treaty between these old enemies and neighbours.

Theory and practice don't always match. Last year's conference was dominated by ill-tempered exchanges between Mahmoud Abbas, the Palestinian president and Israel's prime minister, Ehud Olmert – and that was before the now-faltering negotiations were launched at Annapolis in November.

The Petra agenda this time was supposed to be strictly non-political. Laureates as different as the Dalai Lama and Northern Ireland's David Trimble were on hand to offer leadership and insights. Yet it still proved impossible to escape the shadow of the conflict across the river Jordan.

Shimon Peres, Israel's president (and Nobel peace prizewinner), was ambushed at the opening session by Amr Musa, the secretary-general of the Arab League, who questioned whether continuing settlement activity in the West Bank and a refusal to accept the 2002 Arab peace initiative meant that Israel was sincere. "You are a great speaker, Mr President," Musa told the veteran Israeli politician, "but please don't take us for granted."

Peres retorted that Israel had given Egypt and Jordan "everything" they had wanted in exchange for the peace agreements they had signed - and attacked the Islamists of Hamas for carrying on shooting after Israel withdrew unilaterally from the Gaza Strip three years ago.

The sudden, unscripted spat sent a ripple of unease through the audience, some of whom felt this raw political discord was inappropriate. Others, including senior Jordanians, welcomed Musa's acerbic intervention, which made headlines in the Arab and Israeli media.

For the record, King Abdullah also made some anodyne remarks about the urgency of creating a Palestinian state - but diplomatically refrained from criticising Israel. "It would be a serious mistake to miss the opportunities we have this year to establish, finally, a sovereign, independent and viable Palestinian state along with a secure and recognized Israel," he warned. It is a speech he has made many times before.

Palestine just kept coming up: a young Palestinian scientist complained that Israeli settlers in the West Bank consumed four times as much water as their Palestinian neighbours, and pointed to the problems caused by the "apartheid wall" – what the Israelis call their "security barrier".

In a session on culture another Palestinian insisted it was impossible to keep art and politics separate when living under occupation. Breakfast for university professors was marred when an Israeli who talked about academic cooperation was rebuffed by an Arab insisting that freedom had to come first. When it came to energy conservation someone observed that Palestinians wasted vast amounts by being forced to wait at Israeli army checkpoints. And so it went on.

In a media panel the al-Hayat columnist Jihad al-Khazen brandished the latest casualty figures to demonstrate that Israel was seven times more "terrorist" than the Palestinians.

Several Arabs protested that Israel was not content with occupying Palestinian land but had even appropriated Palestinian food, billing dishes such as hummus, falafel and tabbouleh as "authentically Israeli". Leon Wieseltier, a leading American Jewish literary figure, suggested gently that this was in fact an example of the "levantinisation" of Israel – "a way of living in this region." Noone responded.

"It reminded me of a couple going through the early stages of divorce proceedings," mused another participant. "Every time they began to discuss something one side would start complaining furiously about something unrelated that the other had done."

It all highlighted the awkward position that Jordan has been in since Abdullah's father, Hussein (memorably described by Peres as "his royal shyness") made his peace with Israel. Jordan annexed the West Bank in 1950, ruled it until the 1967 war but relinquished its claim in 1988. The two countries had long been "the best of enemies" in secret but it was only after Yasser Arafat led the PLO into the ill-fated Oslo agreement with Israel that they went public and signed their treaty in 1994. Hussein famously wept when Yitzhak Rabin was assassinated by an Israeli extremist a year later.

The commitment to dialogue lives on: thus the Petra partnership with Wiesel, whose stock-in-trade is the Nazi Holocaust and human suffering. The presence of other American Jews and Israelis was on a scale that would be inconceivable in Egypt, which pioneered Arab acceptance of Israel when Anwar Sadat signed his treaty in 1979.

It is the way of such conferences that the event itself matters more than any outcome – though this year saw the launch of a $10m (£5m) Middle East Scientific Fund to promote graduate research. The inspiring educational success of the Nobel laureates, argued the king, "is the strongest answer to those who preach destruction, isolation and cynicism."

Wiesel had the last word: "Whatever brings Palestinians and Israelis together, I am for," he said. "Whatever brings Arabs and Jews together, I am for. I am a matchmaker. That's my privilege and my vocation." These are noble sentiments but ones that still struggle to overcome the region's great divide.