President Obama meets with Russian President Vladimir Putin in Enniskillen, Northern Ireland, on June 17, 2013. (Evan Vucci/AP)

President Obama has not met one-on-one with President Vladimir Putin for more than 15 months but agreed Thursday to sit down with the Russian leader in New York on Monday as part of a broader effort to resolve the conflicts in Syria and Ukraine.

The session, which will take place on the sidelines of the U.N. General Assembly next week, acknowledges Putin’s considerable influence on the world stage, despite a lengthy effort by the administration to punish Russia, diplomatically and economically, for its annexation of Crimea last year and for its support of the forces that have seized portions of Ukraine.

It also underscores the rising alarm over Russia’s stepped-up military involvement in Syria at a time when Obama’s Syria policy has yet to produce tangible gains.

White House press secretary Josh Earnest said that the meeting came at Putin’s request and that at the top of the agenda for Obama will be Ukraine, where, he said, Russian separatist troops remain in “clear violation of the territorial integrity of that sovereign nation.”

Celeste Wallander, the National Security Council’s senior director for Russia and Eurasia, said the “face-to-face” talk between Obama and Putin would give them a chance to discuss not only the situation in Ukraine, but also what Russia is willing to do to counter Islamist extremism and forge a resolution to the conflict in Syria.

“So there’s a lot of talk, and now it’s time for clarity and for Russia to come clear — come clean and come clear on just exactly how it proposes to be a constructive contributor to what is already an ongoing multi-nation coalition,” Wallander said.

The two leaders last spoke by phone in July after negotiators from Iran and six world powers, including the United States and Russia, reached an agreement to limit Iran’s nuclear program. Their longest recent face-to-face meeting was a 15-minute conversation during the D-Day commemoration in June 2014; they spoke in passing at a November 2014 summit of the Asia-Pacific Economic Cooperation group in Beijing.

The White House issued a statement saying that despite differences in policy, the two leaders needed to discuss Russia’s recent military reinforcement of embattled Syrian President Bashar al-Assad and continuing violations of a cease-fire accord for Ukraine that was negotiated by Russian, Ukrainian and European leaders in Minsk, the capital of Belarus.

Earnest said that when the two leaders talk about Syria, Obama would encourage Russia to join coalition efforts to combat the Islamic State but warn that “doubling down on the Assad regime is a losing bet.” He added that “a face-to-face sit-down seems appropriate at this juncture.”

Yet Russia’s decision to escalate its military intervention in Syria has complicated the conflict there, with administration officials saying repeatedly they are unsure of Moscow’s intentions. One theory is that the Russians are trying to preserve Assad as the power in Damascus. Another is that they are prepared eventually to jettison Assad but want to position themselves for a negotiated end game.

The administration says it has no interest in Putin’s still-vague proposal for Syria — that the West drop its insistence that Assad must go and that all parties join together to defeat the Islamic State. But administration officials still believe there are grounds for U.S.-Russian cooperation there, if Putin is willing.

Michael McFaul, who served as U.S. ambassador to Russia between December 2011 and February 2014, said in an interview that the decision to meet with Putin reflected Obama’s long-standing belief that he needed to engage with adversaries to advance his objectives overseas.

“President Obama wants to have a better understanding of Putin’s objectives in Syria,” said McFaul, who now directs Stanford University’s Freeman Spogli Institute for International Studies and is a senior fellow at the Hoover Institution.

Senior officials said that Obama is prepared to reaffirm the U.S. position that it does not seek the destruction of the Syrian military, and that the rapidly changing Syrian landscape — particularly the growth of the Islamic State and the expanding humanitarian crisis — means there are overlapping U.S. and Russian interests.

Philip Gordon, a senior fellow at the Council on Foreign Relations who served as the White House coordinator for the Middle East, North Africa and the Gulf Region from 2013 to 2015, said that Russia’s deeper involvement in Syria might make Moscow more comfortable about a political future without Assad.

“If nothing else, this has opened up a new phase of the diplomacy,” Gordon said. “It’s pretty clear that we’re not on the verge of putting together a force capable of bringing about the transition we’ve been working on for so long.”

Even McFaul, who has advocated for engagement with Putin, emphasized a need to have “low expectations” of what the conversation could produce. “Don’t have any illusions that this will lead to a breakthrough on Syria, or Ukraine, or U.S.-Russia relations,” he said.

In Ukraine, while violence has notably decreased in recent weeks, there has been no progress toward a political solution. The most immediate U.S. focus is on an upcoming Oct. 2 summit among the negotiators of the Minsk agreements — Germany, France, Ukraine and Russia.

“Those negotiations are not going well,” said Andrew Weiss of the Carnegie Endowment for International Peace. German Chancellor Angela Merkel, Putin’s primary interlocutor on Ukraine, is “distracted by the migration crisis, and Ukraine has tumbled to a third-tier priority,” he said

The United States and European nations imposed economic sanctions on Russia after the annexation of Crimea, and those sanctions are still in effect. They limit investments and dealings with major state-owned companies and prominent individuals.

“The White House keeps hoping Putin will come back from the dark side,” said Stephen Sestanovich, senior fellow at the Council on Foreign Relations who also was U.S. ambassador at large for the former Soviet Union. “It’s an understandable hope, and the reason [Secretary of State John F.] Kerry went to Sochi in May. But the president should remember two things about that visit: Nothing positive came out of it, and the Russians went out of their way to embarrass Kerry. This could turn out differently, but Obama should be ready for the same old, same old.”

Karen DeYoung contributed to this report.