President Obama gives his vision of US leadership to UN
President Barack Obama has laid out a broad vision of American leadership in a changing world, in a UN speech.
He told the UN General Assembly the world needs a new blueprint to deal with the terror, conflict, climate and health challenges it faces.
The president said the Ebola outbreak, Islamist militancy and Russian aggression needed addressing.
He added the world was at a crossroads between "war and peace", "disorder and integration", and "fear and hope".
Mr Obama told representatives of 193 nations, "On issue after issue, we cannot rely on a rule-book written for a different century."
"If we lift our eyes beyond our borders - if we think globally and act co-operatively - we can shape the course of this century as our predecessors shaped the post-World War Two age."
Sharply critical of Russian actions in Ukraine, Mr Obama said it was an example of what happens when countries do not respect international laws and norms.
He called on Russian President Vladimir Putin to follow "the path of diplomacy and peace and the ideals this institution is designed to uphold".
Analysis - Nick Bryant, BBC News, New York
When President Obama addressed the UN General Assembly 12 months ago, he spoke of Iraq mainly in the context of America's withdrawal - a country in his rear-view mirror.
Yet the fight in Iraq and Syria against Islamic State, a militant group he once likened, derisively, to a junior basketball team, could dominate his remaining years in office.
America would not base its entire foreign policy on reacting to terrorism, he stressed, but it is certain to take up much of the remaining bandwidth.
The phrase that will linger is "the network of death", but Mr Obama was at pains to point out this is no clash of civilisations. Nor is America acting alone. More than 50 nations will contribute to the fight against Islamic State.
That fight, he said, needs to be ideological as well as military. He called for a new compact among civilised peoples to "eradicate war at its most fundamental source - the corruption of young minds by violent ideology".
He also addressed the challenges of tackling Ebola in West Africa, forming a strong international coalition on climate change and moving forward on nuclear talks with Iran.
And he said that too many Israelis are ready to abandon "the hard work of peace" in the region and that was something on which the country should reflect.
But his speech was dominated with what he described as the "cancer" of extremism in the Islamic world.
"We reject any suggestion of a clash of civilisations," he said.
"Belief in permanent religious war is the misguided refuge of extremists who cannot build or create anything, and therefore peddle only fanaticism and hate."
In his speech he called on the world to join him in this effort to degrade and ultimately destroy this militant organisation, what he described as a "network of death".
The president outlined America's role as the lead player in a coalition of more than 50 countries committed to defeating Islamic State militants.
The US has carried out more than 194 air strikes against the militants in Iraq since August.
On Monday, Mr Obama extended these strikes into Syria, joined by the Arab nations Bahrain, Saudi Arabia, Jordan and the United Arab Emirates.
Qatar played a supporting role in the military action.
Mr Obama also spoke about the need to tackle the roots of terrorism, and the importance of offering alternatives to young people who are attracted to militancy.
Mr Obama admitted the US had sometimes failed to live up to its ideals but said he welcomed the world's scrutiny.
The US, he said, held "an unyielding belief in the ability of individual men and women to change their communities and countries for the better".
Opening the debate, UN Secretary General Ban Ki-moon warned that human rights were "under attack".
"From barrel bombs to beheadings, from the deliberate starvation of civilians to the assault on hospitals, UN shelters and aid convoys, human rights and the rule of law are under attack," he told the assembly.
Jordan's King Abdullah II said his country was facing an "overwhelming burden" because of the 1.4 million Syrian refugees who had fled there.
"The refugee crisis is recognised global responsibility, and demands a global solution," he said.
"There must be a concerted effort to get humanitarian assistance flowing inside Syria, and to support host countries and communities including Jordan."
But not all of Wednesday's speeches focused on the threat from Islamic militants.
The first speech of the day from Brazilian President Dilma Rousseff urged action on the recent economic crisis.
"It is vital and urgent to restore the dynamism of the global economy, which should work towards fostering investment, international trade, and the reduction of inequalities among countries," she said.