President Barack Obama has told the United Nations that he will build a coalition to "dismantle this network of death" amid a US-led bombing campaign against Islamic State militants.
Mr Obama told the assembled leaders that the "only language understood by killers like this is the language of force".
In remarks prepared for delivery, the president warned those who have joined the Islamic State (IS) to "leave the battlefield while they can".
After weeks of launching strikes against militant targets in Iraq, Mr Obama extended the military action into Syria on Monday.
The US was joined by a coalition of five Arab nations.
Mr Obama told the annual gathering of the UN General Assembly that the US would be a "respectful and constructive partner" in confronting the IS militants through force.
But he also implored Muslims in the Middle East to reject the ideology that has spawned groups like IS and to cut off funding that has allowed that terror group and others to thrive.
"Ultimately, the task of rejecting sectarianism and extremism is a generational task - a task for the people of the Middle East themselves," Mr Obama said. "No external power can bring about a transformation of hearts and minds."
The president's remarks came against the backdrop of an expanded US military campaign against the Islamic State group, with air strikes now hitting targets in both Iraq and Syria.
Bahrain, Jordan, Saudi Arabia, the United Arab Emirates and Qatar also joined the US this week in the strikes in Syria.
The US also opened another military front with air strikes this week against a new al Qaida cell that the Pentagon said was "nearing the execution phase" of a direct attack on the US or Europe.
The threats have drawn Mr Obama back into conflicts in the Middle East that he has long sought to avoid, particularly in Syria, which is mired in a bloody civil war. Just months ago, the president appeared to be on track to fulfil his pledge to end the US-led wars he inherited in Iraq and Afghanistan.
Mr Obama sought to distinguish this current military campaign from those lengthy wars, declaring that he has no intention of sending US troops to occupy foreign lands.
"We will neither tolerate terrorist safe havens nor act as an occupying power," he said.
The militant threat in the Middle East is just one in a series of global crises that have tested Mr Obama this year.
Russia has repeatedly flouted warnings from the US and Europe to stop its threatening moves in Ukraine. And leaders in West Africa have criticised Mr Obama for not doing more to help combat an Ebola outbreak that is believed to have infected more than 5,800 people in Liberia, Sierra Leone, Guinea, Nigeria and Senegal.
Mr Obama took on Russia directly in his remarks, accusing Moscow of sending arms to pro-Kremlin separatists, refusing to allow access to the site of a downed civilian airliner and then moving its own troops across the border with Ukraine.
"This is a vision of the world in which might makes right, a world in which one nation's borders can be redrawn by another, and civilized people are not allowed to recover the remains of their loved ones because of the truth that might be revealed," Mr Obama said. "America stands for something different."
Still, Mr Obama held open the prospect of a resolution to the conflict between Russia and Ukraine. While he has previously expressed scepticism about a fragile ceasefire signed earlier this month, he said that the agreement "offers an opening" for peace.
If Russia follows through on the agreement, Mr Obama said the US will lift economic sanctions that have damaged Russia's economy but so far done little to shift President Vladimir Putin's approach.
As Mr Obama spoke, Russian foreign minister Sergei Lavrov sat in the audience at the UN, staring down at a stack of papers without glancing up at Mr Obama.
The chaotic global landscape Mr Obama described stood in contrast to his remarks at the UN one year ago, when he spoke of diplomatic openings on multiple fronts.
At the time, the US was embarking on another attempt to forge an elusive peace between Israelis and Palestinians and there were signs of a thaw in the decades-old tensions between the US and Iran.
The Mid East peace talks have since collapsed, though the president said that "as bleak as the landscape appears, America will never give up the pursuit of peace".
And while the US, Iran and world powers are now in the midst of nuclear negotiations, the talks are deadlocked and there is scepticism about whether a deal can be reached by a November 24 deadline.
"My message to Iran's leaders and people is simple: Do not let this opportunity pass," Mr Obama said. "We can reach a solution that meets your energy needs while assuring the world that your programme is peaceful."