UNITED NATIONS — President Obama on Tuesday laid down a retooled blueprint for America’s role in the strife-torn Middle East, declaring that the United States would use all of its levers of power, including military force, to defend its interests, even as it accepted limits on its ability to influence events in Syria, Iran and other countries.

In a wide-ranging speech to the General Assembly that played off rapid-fire diplomatic developments but also sought to define what he called a “hard-earned humility” about American engagement after 12 years of war, Mr. Obama insisted that the United States still played an “exceptional” role on the world stage. Turning inward, he said, “would create a vacuum of leadership that no other nation is ready to fill.”

Mr. Obama embraced a diplomatic opening to Iran, saying he had instructed Secretary of State John Kerry to begin high-level negotiations on its nuclear program. He called on the Security Council to pass a resolution that would impose consequences on Syria if it failed to turn over its chemicals weapons.

And he delivered a pitch for peace talks between Israel and the Palestinians, talks that have restarted at the prodding of Mr. Kerry.