UNITED NATIONS — President Obama and Russian President Vladimir Putin laid out sharply competing visions Monday about how to tackle conflicts in Syria and elsewhere in the Mideast, with each blaming the other for the region’s turmoil even as they signaled a willingness to address it together.

In speeches to the U.N. General Assembly less than two hours apart, each leader embraced a foreign policy approach that respects international norms that, they said, are essential to global stability. They sharply differed on whether Syrian President Bashar al-Assad should continue to lead that nation.

Later in the day, the two met privately to hash out their differences and see whether there was room for cooperation. The closed-door session lasted one hour, 40 minutes, ending just before Obama was scheduled to host a reception for delegates.

In his speech, Obama alluded to Russia’s military buildup in Syria as well its support for Ukrainian separatists. “We are told that such retrenchment is required to beat back disorder, that it’s the only way to stamp out terrorism, or prevent foreign meddling,” Obama said. “But I stand before you today believing in my core that we, the nations of the world, cannot return to the old ways of conflict and coercion. We cannot look backward. … And if we cannot work together more effectively, we will all suffer the consequences.”

Putin, for his part, charged that attempts by Western nations to impose democracy – including in Iraq and Libya – were responsible for upheaval in the Middle East and North Africa. While people in those regions clearly wanted and deserved change, “the export of revolutions, this time so-called democratic ones,” had resulted in “violence and social disaster” instead of a “triumph for democracy,” he said.

Then Putin had a question: “I cannot help asking those who have forced this situation, do you realize now what you have done?” he said in remarks clearly directed at the United States. “Policies based on self-conceit and belief in ones’ exceptionality and impunity have never been abandoned.”

Beyond the barbs, the two raised the prospect of cooperating more closely on fighting Islamist terrorists and brokering a political solution in Syria, where war has raged for 4 ½ years. Obama and Putin – who opened their first extended, formal meeting in two years Monday evening with a stiff, largely unsmiling handshake before the cameras – remain divided over whether Assad should have a role in fighting militants or leading Syria.

Obama said Assad must go as part of any resolution, while Putin continues to support the Syrian leader.

“The United States is prepared to work with any nation, including Russia and Iran, to resolve the conflict,” Obama said in his 42-minute speech. “But we must recognize that there cannot be, after so much bloodshed, so much carnage, a return to the prewar status quo. Let’s remember how this started.”

But Putin insisted that “no one but Assad’s forces and militias are truly fighting the Islamic State.” He said it would be an “enormous mistake to refuse to cooperate with the Syrian government and its armed forces.”

Russia has directly challenged U.S. military and diplomatic dominance in the region and the U.S.-led coalition air campaign against the Islamic State in Iraq and Syria. Over the past month, Putin has expanded Russia’s long-running provision of weapons to Assad with deployments of tanks and aircraft. Last week, Russia and Iraq announced they would establish a rival anti-militant coalition in Baghdad to include Iran and Syria.

Russia maintains that Western intervention in Syria is a violation of international law.

“On the basis of international law,” Putin said, “we must join efforts to address the problems that all of us are facing, and create a genuinely broad international coalition.”

He compared it to the Allied powers that won World War II. “Similar to the anti-Hitler coalition, it could unite a broad range of forces that are resolutely resisting those who, just like the Nazis, sow evil and hatred of humankind,” Putin said. “And, naturally, the Muslim countries are to play a key role in the coalition, even more so because the Islamic State does not only pose a direct threat to them, but also desecrates one of the greatest world religions by its bloody crimes.”

RUSSIAN INITIATIVE MAKES GAINS

Russia, the current chair of the U.N. Security Council, has called for a meeting next month to discuss how to better combat extremism. Moscow has also proposed a meeting among itself, the United States, and the governments of Iran, Syria, Saudi Arabia, Turkey and Egypt on coordination over Syria.

The Obama administration has not yet responded to the latter proposal, and it remains unclear whether Saudi Arabia, the most powerful Sunni Arab state opposed to Assad, and Iran, the Syrian leader’s other main backer, would agree to cooperate on any Syrian initiative.

Leading European members of the U.S.-led coalition, who have been conducting air attacks against the Islamic State in Iraq and Syria over the past year, have indicated that they believe the idea – and some cooperation with Russia – is worth exploring.

French President François Hollande, who last week authorized his country’s first air attacks in Syria, said Monday that “today, the moderate opposition is weak, Bashar al-Assad is weak, and ISIL is strong.” ISIL is one of several acronyms for the Islamic State. “We can’t stick to our original enemies,” Hollande said to reporters. “We have to gather everybody together.”

“If Saudi Arabia and Iran can find agreement on the future of Syria, then there can be an answer,” Hollande said.

In comments last week, British Prime Minister David Cameron and German Chancellor Angela Merkel appeared to be softening their position toward Assad, at least temporarily. “We have to speak with many actors; this includes Assad, but others as well,” Merkel said. “Not only with the United States of America, Russia, but with important regional partners, Iran, and Sunni countries such as Saudi Arabia.”

REFUGEES INFLUENCE EUROPE’S VIEW

European views have been influenced not only by the stagnation in the Syrian conflict, now in its fifth year, and Islamic State’s expansion in Iraq, but also by the hundreds of thousands of refugees – many from Syria – who have been pouring into their countries.

U.N. Secretary General Ban Ki-moon praised European countries that have provided asylum but urged them to do more. “After the Second World War, it was Europeans seeking the world’s assistance,” Ban said.

Obama and Putin also offered differing accounts of what had transpired in Ukraine, where Russia has annexed Crimea and backed separatists in the country’s southeast.

Although Putin devoted the bulk of his speech to Syria and terrorism, he repeated Russia’s charge that the overthrow of Ukraine’s government early last year was “orchestrated from outside.” He said Russia would adhere to the Minsk agreements, if they represent the legitimate demands of eastern Ukraine separatists that Moscow has backed.

Obama, however, said the West would continue to impose economic sanctions on Russia unless it reversed course. “We cannot stand by when the sovereignty and territorial integrity of a nation is flagrantly violated.”