In a phone call, they welcomed "the implementation of the ceasefire in Syria," the ministry said in a statement yesterday.
"They also discussed the outlook for resuming the peace negotiation process in the framework of the International Syria Support Group (ISSG)," Moscow said, adding that both sides recognised the "particular importance" of working together as co-chairs of the 17-nation group.
Lavrov and Kerry also discussed "ways for ensuring it (the ceasefire) is fully upheld, including enhancing military cooperation between Russia and the United States," the statement said.
"They agreed that while initial reports have been encouraging, a serious effort by all parties will be critical to success going forward," Kirby added.
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"They also reaffirmed their commitment to implementing the cessation of hostilities and to delivery of needed humanitarian aid to communities across Syria."
The Russian military earlier said its warplanes had suspended all sorties over Syria on Saturday to avoid any "bombing mistakes" and the US and Russia militaries also exchanged maps of Syria.
It is the first major truce in a five-year war that has claimed 270,000 lives and displaced more than half of Syria's population.
The agreement calls for the cessation of hostilities between the forces of Russian-backed President Bashar al-Assad and opposition groups, but it does not cover jihadist groups such as the Islamic State and Al-Nusra Front.
UN envoy Staffan de Mistura has said peace talks -- suspended since February 3 amid a regime offensive backed by Russian air power -- will resume on March 7 if the ceasefire prevails and more aid is delivered.