Speaking to the U.N. General Assembly, President Obama outlined steps that world leaders should take against violent extremists such as the Islamic State militants. He also criticized Russia for its conflict with Ukraine. (AP)

Seeking to reassert American leadership abroad, President Obama challenged world leaders Wednesday to join the United States in confronting a series of crises he described as having created a “pervasive sense of unease” across the globe.

“There is much that must be done to meet the tests of this moment,” Obama said in an address at the annual U.N. General Assembly. He cited the Ebola outbreak in West Africa, Russian aggression in eastern Ukraine and the threats of the Islamic State group in the Middle East.

“We come together at a crossroads between war and peace; between disorder and integration; between fear and hope,” the president declared.

In a 40-minute address that served as the centerpiece of his three-day visit here, Obama delivered a forceful, and at times searing, critique of the threats to international order that he said required collective attention and action from the more than 150 countries assembled at the United Nations. The tone of the remarks contrasted sharply with Obama’s address here last year when he said that “the world is more stable than it was five years ago.”

His appearance on stage Wednesday was also a bid to recruit more nations to actively support a U.S.-led coalition in combating the radical Islamist fighters who have taken control of large swaths of Iraq and Syria.

By the afternoon, Obama’s efforts appeared to be paying some dividends, as British Prime Minister David Cameron recalled parliament to vote Friday on a provision to authorize that country to join the U.S. airstrikes in Iraq — with approval looking likely, although the British will not consider participating in strikes in Syria. And the U.N. Security Council, in a rare meeting chaired by Obama, approved a binding resolution that would require member nations to enact laws aimed at preventing their citizens from traveling to foreign countries to join terrorist insurgencies.

The U.S.-drafted measure unanimously approved by the 15-member Security Council was a response to the rapid rise of the Islamic State but applies to those who might travel to join any terror group. It also tells U.N. member states to clamp down on recruitment and funding for terrorist groups.

The resolution strengthens the legal framework for international action in response to the threat posed by foreign fighters, and requires countries to “prevent and suppress recruiting, organizing, transporting, and equipping” of terrorist fighters, and the financing of their travel and activities. It also asks members to do more to cooperate with one another and share criminal or other information where appropriate.

Obama told the council that some 15,000 fighters from more than 80 nations have traveled to Syria and Iraq to join the Islamic State or the al-Qaeda affiliate known as Jabhat al-Nusra. U.S. officials estimate that among that number were 2,000 Europeans and 100 Americans. Fears that they could return to their homelands and perpetrate domestic terrorist attacks spurred Obama to raise the issue to international attention at the summit, aides said.

“Resolutions alone will not be enough,” Obama said after the resolution was adopted. “Promises on paper cannot keep us safe. Lofty rhetoric and good intentions will not stop a single terrorist attack. The words spoken here today must be matched and translated into action. . . . For if there was ever a challenge in our interconnected world that could not be met by one nation alone, it is this: terrorists crossing the border to unleash terrible violence.”

Even as the president was making progress on building the international coalition, he and the other world leaders were reminded of the magnitude of the challenge when an al-Qaeda splinter group revealed that it had beheaded a French citizen in Algeria. France has agreed to assist the U.S. airstrikes in Iraq but not Syria.

“In the face of barbarism, force is not only necessary, but it is legitimate,” French President François Hollande said during the Security Council meeting.

Republicans and some Democrats have accused Obama of failing to assert U.S. power and influence more decisively, particularly in Ukraine and the Middle East. And Obama’s approval ratings on foreign policy are at an all-time low.

Obama and his advisers have cautioned that the president is prepared to act with force to defend American interests but seeks to build international support ahead of time. On Wednesday, Obama had a bilateral meeting with new Iraqi Prime Minister Haider al-Abadi, who took power after the United States helped force the resignation of his predecessor Nouri al-Maliki, whose inability to bridge rival Muslim factions has been blamed for allowing the Islamic State group to advance through the western portion of the country from Syria.

In his remarks, the president cast the crises on three different continents as part of a broader breakdown in international institutions charged with maintaining peace and security. He repeatedly asserted the United States’s leadership role in confronting those global challenges, urging others to join America “on the right side of history.”

“Too often, we have failed to enforce international norms when it’s inconvenient to do so,” he said. “And we have not confronted forcefully enough the intolerance, sectarianism and hopelessness that feeds violent extremism in too many parts of the globe. . . . On issue after issue, we cannot rely on a rulebook written for a different century.”

[Read: Transcript of Obama’s speech]

Obama spent the second half of his address focused on the problem of confronting terrorism and radical ideology that has led to the rise of the Islamic State group in Iraq and Syria. He authorized U.S. military action to degrade the Islamic State group in Iraq and Syria, and the Pentagon launched the first airstrikes in Syria this week in conjunction with five Arab nations — Saudi Arabia, Jordan, Bahrain, the United Arab Emirates and Qatar.

“I have made it clear that America will not base our entire foreign policy on reacting to terrorism,” Obama told the U.N. delegates. But, referring to the radical Sunni militants, he added that “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 also castigated Russian President Vladi­mir Putin, who skipped the U.N. summit, by denouncing the Russian-backed incursion of rebel fighters in eastern Ukraine, which the president said demonstrated a “vision of the world in which might makes right.”

Toward the end of his speech, Obama also touched on problems in the United States, highlighting the racial unrest in Ferguson, Mo., this summer after an unarmed African American teenager was shot and killed by a white police officer after a scuffle. Protests on the streets of the community lasted for nearly two weeks, leading to scores of arrests and a visit from U.S. Attorney General Eric H. Holder Jr., who is overseeing a federal civil rights probe into the Ferguson police department’s actions.

“I realize that America’s critics will be quick to point out that at times we, too, have failed to live up to our ideals; that America has plenty of problems within our own borders. This is true,” Obama said. “In a summer marked by instability in the Middle East and Eastern Europe, I know the world also took notice of the small American city of Ferguson, Missouri — where a young man was killed and a community was divided. So yes, we have our own racial and ethnic tensions. And like every country, we continually wrestle with how to reconcile the vast changes wrought by globalization and greater diversity with the traditions that we hold dear.”

Anne Gearan contributed to this report.