Few speeches have been as eagerly awaited in the Middle East as President Obama's address in Cairo University to the Muslim world. And few speeches have been as carefully crafted, as powerfully delivered or as comprehensive in charting a new beginning between civilisations locked for the past decade in destructive mutual incomprehension. If the President's promises could be delivered, if his aspirations could be achieved and if his respectful tone could be adopted across the region, many of the toxic issues roiling the Middle East might become less intractable.

One speech, as he acknowledged, cannot alone remove the obstacles or soften the animosities that have built up over decades. What it can do is to lay out intent, demonstrate engagement and win the respect of an audience that has come to expect only the worst from America.

Mr Obama has shown extraordinary strength and sensitivity in understanding how America's soft power must be used to achieve what eluded the use of military might. From the opening traditional Muslim greeting to his final and apposite quotations from the Koran, the Torah and the Bible, he showed himself at ease with Islamic culture and customs. He referred to his own name, Muslim forebears and personal memories of Muslims in Indonesia and Chicago; he reminded his audience - and the West - of civilisation's debt to Muslim learning; and he dismissed the crude stereotypes that America and the Islamic world now have of each other with telling examples of past tolerance and engagement.

Having set the tone of respect essential for any hard discussion of differences, he then spoke to the Muslim world - not at it as his predecessor had done. He went straight to the heart of the Middle East's chronic issue, telling the Palestinians and others that violence achieved nothing and that repeating vile anti-Semitic stereotypes was deeply wrong. But he admitted that the situation for the Palestinian people was intolerable and insisted that America would not turn its back on the “legitimate” aspiration of Palestinians for dignity and a state of their own. That will not give comfort to the Netanyahu Government in Israel, nor will his unqualified - and welcome - denunciation of settlements as illegitimate. His skill, however, in saying these things is that he did so in the context of America's strong and enduring relationship with Israel.

The Arabs may have wished for more - for a tougher line on Gaza, a new peace “initiative” and an apology for past US policies. He was right to offer none of these. He did not repudiate his presidential predecessor. Nor did he denounce the two interventions that have inflamed much of the Muslim world - in Iraq and in Afghanistan. Instead, he insisted that America had no wish to stay a moment longer in Afghanistan than the threat dictated. His Administration knew that “the less we use our power, the greater it will be”. But that did not mean that America would not confront extremists.

Like his earlier address to Iran, Mr Obama's appeal struck a chord that infuriated those peddling hatred of America. Both Iran and Osama bin Laden were swift to belittle his words. He did not, sadly, address the issue of democracy. That must remain part of the agenda. What he did was to demolish the myth of a clash of civilisations. That is the first step to bridging the chasm.