Barack Obama's address to "the Muslim world" at Cairo University was a slick public relations exercise, as we have come to expect. But the standing ovation he received was misleading. According to polls, only one in three Egyptians has a favourable opinion of the new man in the White House - Arab mistrust of American foreign policy still runs deep.

The speech was scheduled to maximise the number of Muslims who could watch it live on TV, in the Indonesian or Pakistani evening, or on a North African lunch break. This meant that in New York's "Little Egypt", on Steinway Street in Queens, it was broadcast just after sunrise. By 9am, it was the talk of this strip of hookah bars, pastry shops and halal butchers.

Arab-Americans voted overwhelmingly for Obama in the presidential election, so it came as no surprise that, in a speech notable for its cultural sensitivity, he had greeted them with "As-Salâmu Alaykum" - the standard Arabic greeting of "peace be upon you".

By quoting from the Koran, reminiscing about being woken by the call to prayer as a child and stressing his Muslim lineage on his father's side, Obama gave an assurance that, irrespective of policy, the tone of America's dialogue with Islam has changed.

Mohamed Al Gamssy said: "He's the only US president to consider Islamic civil society. He's trying to mend what has been broken. The speech showed a lot of respect. It showed that he understands Islam is a peaceful religion."

The manager of El Khayam, Godfather of Hookah Lounges', said: "Obama is one of the best presidents of this country. We all vote for him. We trust him to do the right thing."

In terms of substance, there was remarkably little to differentiate Obama's discourse from a much less heralded speech delivered by George Bush "directly to the people across the broader Middle East" in September 2006. Both spoke of the daily humiliations suffered by Palestinians (although only Obama used the word Palestine), insisted somewhat disingenuously that the US would never impose democracy by force and sought to draw a distinction between "violent extremists" and the vast, peaceful Muslim majority.

And Obama made few specific commitments. For instance, although he recognised the "legitimate aspirations" of Palestinians and conceded that Hamas enjoys broad popular support, he stopped short of calling for an end to Jewish settlements in the West Bank and Gaza, widely viewed as a prerequisite for any durable two-state solution.

Last month, Tony Blair said the Middle East Quartet (the US, EU, UN and Russia) would lay out a comprehensive new strategy in "five to six weeks". Obama's speech has created expectations of a newly even-handed approach.

Grocer Ahmed Alfraha, an Egyptian, told me New York's Arab community has high hopes. "When America sees something bad, she must say it is bad," he said. "Even in Israel, she must say it is bad. Maybe she cannot change it at first, but if she is fair, this is important."

Any peace plan that makes major concessions to Palestinians will meet powerful opposition from the Israel lobby, which recently demonstrated its reach by successfully blocking the appointment of Chas Freeman, an opponent of the Israeli occupation, as director of the National Intelligence Council.

The American right is already presenting Obama's efforts at diplomacy as appeasement. On Friday, the cover of the New York Post carried a picture of two masked fighters with machine-guns tuned in to his speech, with the mocking caption: "Let's be friends - Hamas thugs watch Bam woo Muslims."

Arab conservatives were no more conciliatory: Iran's supreme leader Ayatollah Ali Khamenei said "beautiful speeches" could not change the fact that Iranian Muslims "hate America from the bottom of their heart".

But in this brief moment following a genuine attempt by an American president to engage the Muslim world in all its diversity, cautious optimism was the rule, despite the near-impossibility of negotiating a settlement between intransigent enemies in Israel and Palestine, to say nothing of re-engineering the relationship between two entire cultures.

Mona, the young woman behind the counter at the Nile Deli, New York, was impressed by Obama's cultural fluency. "I agree with him. He speaks very well about Islam," she said.

"But will he change anything? I can't answer this question. In two, three years, we will see."