U.S. President Barack Obama called on world leaders to “speak out forcefully against violence and extremism,” saying the world can only make progress by pursuing tolerance and freedom.

Mr. Obama spoke Tuesday to the 67th session of the United Nations General Assembly getting a smattering of polite applause. He told delegates “it is time to marginalize those who – even when not resorting to violence – use hatred of America, or the West.”

Much of his speech focused on the weeks of violent protest sparked by an anti-Muslim film, made it the U.S. Mr. Obama called the video crude and disgusting, but said it did not justify the spilling of any innocent blood, including the U.S. Ambassador to Libya, Chris Stevens, who was killed in an attack on the U.S. consulate in Benghazi.

Mr. Obama vowed the U.S. “will be relentless in tracking down the killers and bringing them to justice.”

The U.S. president also had harsh words for Syrian President Bashar al-Assad, labeling the government “a regime that tortures children and shoots rockets at apartment buildings.”

He also warned Iran the United States “will do what we must” to prevent Tehran from acquiring nuclear weapons. He said there is “still time and space” to negotiate over its nuclear program, but “that time is not unlimited.”

U.N. Secretary General Ban Ki-moon addressed the General Assembly earlier Tuesday, calling on member-nations to do more to ease the crisis in Syria.

He called the conflict in Syria “a regional calamity with global ramifications” and accused both the government of Syrian President Bashar al-Assad and the opposition of crimes against humanity.

The world is deadlocked on how to deal with that conflict, which has killed more than 20,000 people, mostly civilians. Russia and China have vetoed tough sanctions against the Syrian government in the Security Council, and neither the United States nor its allies have thus far called for direct military intervention.

Mr. Ban also admonished world leaders for their reaction to the violent protests that have gripped parts of the Middle East and Asia. He said leaders must do more to diffuse tensions, saying “'too many people are willing to take small flames and…turn them into a bonfire.”

The secretary general deplored the “dangerous impasse” between Israel and the Palestinians that may close the door on a two-state solution, and criticized the rhetoric between Israel and Iran over Tehran's nuclear program.

More than 120 world leaders are set to attend the General Assembly meeting to discuss and debate wars, political crises and humanitarian concerns.