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In a speech to the UN General Assembly in New York, Obama said Islamic State must be destroyed, as British Prime Minister David Cameron weighed whether his country would join the military drive that includes US Arab allies.
Before Obama spoke, US-led airstrikes for the third time this week pounded Islamic State targets.
Obama used graphic language to condemn Islamic State's methods, saying the militants had used rape as a weapon of war, gunned down children, dumped bodies in mass graves, and beheaded their victims.
"No God condones this terror," he said.
"The only language understood by killers like this is the language of force. So the United States of America will work with a broad coalition to dismantle this network of death," he said in a speech that ran to just under 40 minutes.
Obama, whose legacy is based in part on his decision to extract US forces from Iraq, said the United States does not intend to occupy any countries, but "will support Iraqis and Syrians fighting to reclaim their communities."
"Today, I ask the world to join in this effort. Those who have joined ISIL should leave the battlefield while they can," he said, using an acronym for Islamic State.
Obama used his annual address to the 193-nation General Assembly to send messages to Russia to back down from its actions against Ukraine, for Iran to "not let this opportunity pass" to forge a nuclear deal and, indirectly, for China to ease its pressure on its Asia-Pacific neighbors.
In a departure from his prepared text, Obama urged Israel to extend an olive branch to the Palestinians after a summer of violence in Gaza.
Too many Israelis, he said, were ready to abandon the hard work of peace and added that this was something "worthy of reflection within Israel."
"Because let's be clear: the status quo in the West Bank and Gaza is not sustainable. We cannot afford to turn away from this effort," he said.
The "worthy of reflection" comment was unlikely to be warmly received by Israeli Prime Minister Benjamin Netanyahu, who has a rocky relationship with Obama and will meet him at the White House on October 1.
Obama's over-arching message was aimed at bolstering the fight, both militarily and diplomatically, against Islamic State, a group whose rapid rise and seizure of broad swaths of Syria and Iraq have stunned the Middle East.
Cameron was due to set out his position on Islamic State in a speech to the General Assembly on Wednesday night. British government sources have said he may announce this week that Britain is ready to join air strikes and that he plans to seek parliament's approval for such action.
SECURITY COUNCIL RESOLUTION
Many of Islamic State's estimated 30,000 members are foreigners who flocked to the fighting. The UN Security Council was poised to approve a resolution later in the day urging governments to clamp down on the travel and financing of the group.
Obama, who has been stymied in trying to resolve long-festering disputes in the Middle East, called for a broader negotiation in which major powers address their differences directly "rather than through gun-wielding proxies."
On Ukraine, Obama said if Russia took the path of peace and diplomacy, then the United States would lift its economic sanctions and would be prepared to engage in the type of diplomacy that in the past has reduced U.S. and Russian nuclear stockpiles and persuaded Syria to give up chemical weapons.
"That's the kind of cooperation we are prepared to pursue again if Russia changes course," he said.
Russian President Vladimir Putin has shown no inclination thus far to bow to Western demands that he end Russian actions in eastern Ukraine after seizing Crimea earlier this year.
On Iran, Obama said there remains an opportunity to reach an agreement between Tehran and world powers aimed at resolving longstanding differences over Iran's nuclear program, which the Iranians say is not intended to develop a weapon.
"My message to Iran's leaders and people has been simple and consistent: do not let this opportunity pass. We can reach a solution that meets your energy needs while assuring the world that your program is peaceful," he said.
Obama, who travels to Beijing in November, urged countries in the Asia-Pacific, without mentioning China in particular, to resolve their territorial disputes peacefully and in line with international law.
He called for many more countries to make concrete commitments to fight the deadly Ebola outbreak in West Africa.