* Obama seeks "new beginning" with Muslims
* Obama discusses Palestinian-Israel conflict with Mubarak
* Bin Laden issues warning to Muslims
(Updates with Khamenei, Abbas spokesman, adds quotes)
By Ross Colvin and David Alexander
CAIRO, June 4 (Reuters) - President Barack Obama sought a "new beginning" between the United States and Muslims around the world in a major speech on Thursday but offered no new initiative to end the Palestinian-Israeli conflict.
"We meet at a time of tension between the United States and Muslims around the world -- tension rooted in historical forces that go beyond any current policy debate," the U.S. president said in a speech at Cairo University.
"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," he said. "America and Islam are not exclusive, and need not be in competition."
Obama's speech, interrupted by applause and occasional shouts of "we love you", was an effort to restore the tarnished U.S. image among many of the more than 1 billion Muslims around the world, badly damaged by the wars in Afghanistan and Iraq and the treatment of U.S. military detainees.
Highlighting the hostility the U.S. leader faces from some quarters, the supreme leader of Washington's regional arch foe, Iran's Ayatollah Ali Khamenei, said in an address America was "deeply hated" and only action, not "slogans," could change that.
And al Qaeda leader Osama bin Laden, in a message on a website, warned Muslims against alliance with Christians and Jews, saying it would annul their faith and urging them to fight allies of the "infidels."
A spokesman for Palestinian President Mahmoud Abbas, however, said Obama's speech was a "good start" towards a new U.S. policy in the Middle East.
The choice of Cairo for the speech underscored Obama's focus on the Middle East, where he faces huge foreign policy challenges, from trying to restart the Israeli-Palestinian peace process to curbing Iran's nuclear program.
Although the administration tried to lower expectations in recent days about what would be accomplished by the speech, there were high expectations in the region that he would take a tougher line on Israel and follow up his words with actions.
He also offered little specifics on democracy, the rule of law and human rights in the Arab world, issues that many in the region had hoped to hear him address.
Obama, who is hoping to build a coalition of Muslim governments to back his diplomatic moves, affirmed his commitment to a two-state solution to the Israeli-Palestinian conflict.
"That is in Israel's interest, Palestine's interest, America's interest, and the world's interest," he said. "That is why I intend to personally pursue this outcome with all the patience that the task requires."
He said Palestinians had to abandon violence and urged them to acknowledge Israel's right to exist. He also said Israel should stop building settlements in the West Bank.
"The United States does not accept the legitimacy of continued Israeli settlements," he said. "This construction violates previous agreements and undermines efforts to achieve peace. It is time for these settlements to stop."
Obama said Iran should have access to peaceful nuclear power, but it must adhere to the nuclear nonproliferation treaty.
"When it comes to nuclear weapons, we have reached a decisive point," he said. "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."
Discussing the war in Afghanistan, Obama said the United States had no interest in keeping military bases or troops there.
"It is agonizing for America to lose our young men and women. It is costly and politically difficult to continue this conflict," he said, adding they would be brought home if there was confidence extremists would not attack the United States again. "But that is not yet the case."
He criticised Iraq as a U.S. "war of choice that provoked strong differences in my country and around the world" and had ultimately reminded Americans of the need to use diplomacy and build international consensus. (Additional reporting by Cynthia Johnston in Cairo and Zahra Hosseinian in Tehran; Writing by Edmund Blair)