President Obama, right, and Russian President Vladi­mir Putin last spoke face-to-face in November 2015 at the G20 summit in Antalya, Turkey. (Pool/Reuters)

President Obama and Russian President Vladi­mir Putin have agreed to intensify diplomatic and military cooperation to implement a cease-fire and the delivery of aid in Syria, the Kremlin said early Sunday.

A statement from Putin’s office said that Obama initiated a telephone conversation between the two. The White House, which said the call took place Saturday, did not mention increased U.S.-Russia cooperation but said that Obama stressed the importance “of rapidly implementing humanitarian access to besieged areas.” Obama also urged Putin to cease Russia’s air campaign against “moderate opposition forces” in Syria, according to a White House statement released Sunday.

The call came amid reports that at least one siege had been broken with the first delivery of humanitarian aid to the rebel-held Douma area, east of the Syrian capital of Damascus. Douma had been cut off by government troops since 2013. A United Nations spokesperson said from Geneva, where a task force is organizing aid under an agreement reached Friday in Munich, that the Douma delivery was a previously scheduled shipment by the Syrian Red Crescent.

The spokesperson, Jessy M. Chahine, said that it would take at least 72 hours for the new assistance to reach a besieged area after approval has been given by whichever side is blocking access. Steffan de Mistura, the U.N. envoy for Syria who helped negotiate the agreement, had said that “immediate” shipment of humanitarian assistance was expected over the weekend.

In the Munich agreement, Russia pledged to stop bombardment of all but “terrorist” groups in Syria. U.S. and Russian teams are scheduled to meet this week to delineate areas that will be off-limits to the Russian airstrikes — a task made difficult by differences of opinion on which rebel groups represent legitimate opposition to Syrian President Bashar al-Assad. The deal calls for the cease-fire to start by Friday.

Russian Prime Minister Dmitri Medvedev said Sunday that Russia would be willing to stop bombing Aleppo to allow a humanitarian corridor to be instituted only if “the parties involved are willing to lay down arms.”

“When one group stops fighting while the other begins to build on its military success, this is the most dangerous situation,” Medvedev told Euronews.

Secretary of State John F. Kerry, who negotiated the agreement with 16 other countries, including Russia and Iran, which support Assad, said Saturday that Russia must “change its targeting.” Kerry visited the Albanian capital Sunday.

The Kremlin statement said that Putin and Obama had “emphasized the need to establish close working contacts” between Russian and U.S. military officials to fight the Islamic State “and other terrorist organizations.”

During the telephone conversation with Obama, the Russian leader “again emphasized the importance of creating a united anti-terrorist front while giving up double standards,” Putin’s office said.

The White House statement did not provide details of the conversation. It did report that Obama urged Putin to adhere to a cease-fire agreement in eastern Ukraine and to ensure that monitors from the Organization for Security and Cooperation in Europe have full access to all areas of that region.

Since Russia began airstrikes in Syria in the fall, the Obama administration has said that the vast majority of Russian bombs have fallen on U.S.-backed opposition forces rather than the Islamic State. The United States has resisted Russian entreaties to share intelligence and coordinate its own airstrikes against the Islamic State. U.S. officials have said they would limit their defense cooperation with Russia to “deconflicting” flights in Syria’s increasingly crowded airspace.

Administration officials have said there will be no change in that policy until the cease-fire is in place and Russia demonstrates it has stopped bombing the opposition and is ready to support the campaign against the Islamic State.

Michael Birnbaum in Moscow contributed to this report.