Barack Obama today appealed for a new beginning in relations between America and the world's Muslims in a much-anticipated speech in Cairo, while delivering a blunt message to Israel over settlements.

The US president paid tribute to Islam's influence on religion, culture and civilisation, and started with the traditional Arabic greeting assalaamu alaykum – peace be upon you – to thunderous applause. Then in an appeal to form a common front against extremists, Obama said the "cycle of suspicion and discord" between the west and Islam must end.

"I have come here to seek a new beginning between the United States and Muslims around the world: one based upon mutual interest and mutual respect; and one based on the truth that America and Islam are not exclusive," he said.

As expected, Obama made proud reference to his own Muslim roots, mentioning his childhood in Indonesia and waking to the sound of the "azaan" call to prayer. He stressed the common ground between the west and Islam, saying that "Islam has always been a part of America's story".

Obama said Islamic teachings, far from being the source of conflict, could help to bring about peace: "The Holy Qur'an teaches that whoever kills an innocent, it is as if he has killed all mankind; and whoever saves a person, it is as if he has saved all mankind … Islam is not part of the problem in combating violent extremism – it is an important part of promoting peace," he said.

In one of the most eagerly awaited elements of the speech, he issued a tough message to Israel that went down well with his audience: stop building settlements on land claimed by Palestinians.

Marking a change from the Bush administration, Obama said: "Israelis must acknowledge that just as Israel's right to exist cannot be denied, neither can Palestine's. The United States does not accept the legitimacy of continued Israeli settlements. This construction violates previous agreements and undermines efforts to achieve peace. It is time for these settlements to stop."

While Obama had made similar statements to the Israeli prime minister, Binyamin Netanyahu, the tone of his remarks before an Arab audience took on a special resonance.

At the same time he sent a clear message to Palestinian militants to abandon violence, saying: "It is a sign of neither courage nor power to shoot rockets at sleeping children, or to blow up old women on a bus."

The Arab-Israeli conflict, Obama added, "should no longer be used to distract the people of Arab nations from other problems. Instead it must be a cause for action to help the Palestinian people develop the institutions that will sustain their state; to recognise Israel's legitimacy; and to choose progress over a self-defeating focus on the past."

Obama's comments in support of democracy – a burning issue in Egypt and in almost all Arab countries – were non-specific, which may disappoint activists in Egypt and elsewhere, but they were greeted with cheers of support from some members of the audience.

In a clear rejection of the Bush doctrine of regime change and attempts to impose democracy, Obama said: "America does not presume to know what is best for everyone, just as we would not presume to pick the outcome of a peaceful election. But I do have an unyielding belief that all people yearn for certain things: the ability to speak your mind and have a say in how you are governed."

Obama defended his strategies in both Afghanistan and Iraq but made clear he did not wish to maintain a permanent presence in either country.

On the burning issue of Iran and nuclear weapons he issued a stark warning: "We have reached a decisive point. This is not simply about America's interests. It is about preventing a nuclear arms race in the Middle East that could lead this region and the world down a hugely dangerous path."

Unprecedented security measures were in place for Obama's big day, which included a tour of the pyramids on Cairo's outskirts and a medieval mosque. Earlier he spoke to the Egyptian president, Hosni Mubarak, before giving his 45-minute address.

A social media networking blitz by the White House helped publicise the speech in an effort to generate discussion.

The Muslim world largely welcomed the speech, although some said it lacked concrete proposals.

"There is a change between the speech of President Obama and previous speeches made by George Bush," said Fawzi Barhoum, a Hamas spokesman in Gaza, "... but the statements of today did not include a mechanism that can translate his wishes and views into actions."

In Iran, Mohammad Ali Abtahi, a cleric who was vice-president under the reformist president, Mohammad Khatami, called the speech "compensation to the hostile environment which was created during President Bush".

The director of Israel's government press office, Danny Seaman, said Obama's speech was "not bad".

"All in all, his attitude is one we certainly share as a democratic country," he said. "The state of Israel isn't against reconciliation ... We think we should be more cautious and it should be done in such a way that the extremists shouldn't take control," he said.

Following his recording yesterday, Osama bin Laden, the al-Qaida leader, to told Muslims that alliances with Christians and Jews would annul their faith. He called on them to fight allies of the "infidels" in Muslim countries.