Addressing the UN General Assembly, U.S. President Barack Obama has called on the world to help destroy the Islamic State (IS) militants' "network of death" and to stand up for Ukraine's sovereignty against Russia's "aggression."
The Ukraine crisis assumed a central spot in the U.S. president's wide-ranging September 24 speech, in which he called on the global community to enforce "international norms."
Obama said Russia's annexation of Crimea in March harks back to an era "when large nations trampled small ones in pursuit of territorial ambition."
Reiterating Washington's stance that Russia is fueling an armed separatist movement in eastern Ukraine and has moved its own troops across the border, Obama vowed to continue a push for international pressure on Moscow.
"We will impose a cost on Russia for aggression, and we will counter falsehoods with the truth," he said.
But the U.S. president also expressed hope that a recent cease-fire between government forces and pro-Russian separatists could bring a lasting peace if the Kremlin complies with it.
"If Russia takes that path -- a path that for stretches of the post-Cold War period resulted in prosperity for the Russian people -- then we will lift our sanctions and welcome Russia's role in addressing common challenges," Obama said.
He added that the United States and its allies "will support the people of Ukraine as they develop their democracy and economy."
"We call upon others to join us on the right side of history -- for while small gains can be won at the barrel of a gun, they will ultimately be turned back if enough voices support the freedom of nations and peoples to make their own decisions," Obama said.
WATCH: Obama Says America And Its Allies Will Support Ukraine
Turning to the subject of extremism and terrorism, Obama vowed to keep up the military pressure on IS militants, amid a U.S.-led international air campaign against the group in Iraq and Syria.
"There can be no reasoning -- no negotiation -- with this brand of evil," Obama 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."
Obama said the United States would be a "respectful and constructive partner" in confronting the IS militants through force.
He also called on Muslims to "explicitly, forcefully, and consistently reject" the group's ideology.
"Ultimately, the task of rejecting sectarianism and extremism is a generational task -- a task for the people of the Middle East themselves," he added.
Obama insisted that that Americans have never been and will never be "at war with Islam."
In his speech, the U.S. president also called on Iran to take advantage of ongoing nuclear talks to find a "diplomatic resolution" to its deadlock with world powers.
Obama said, "My message to Iran's leaders and people has been simple and consistent: do not let this opportunity pass."
Nuclear talks between Iran and Britain, China, France, Russia, the United States, plus Germany have been stalled for months.
The six world powers want Iran to scale down nuclear activities so that it cannot produce nuclear weapons.
Tehran, which denies trying to develop such weapons, wants UN and Western sanctions to be lifted.