The two, over a phone call, discussed humanitarian aid issues and the planned cessation of hostilities in Syria, "with the exception of fighting against terrorist groups".
It was noted that progress was made on humanitarian aid delivery to besieged areas in Syria, Xinhua news agency reported.
Lavrov and Kerry also discussed current practical interaction between the two countries, both being co-chairs of the International Syria Support Group.
"It was confirmed that the establishment of mechanisms to implement tasks (in the Munich agreement reached last Friday) requires military coordination," Russian foreign ministry statement said.
Lavrov also stressed the importance of not allowing Turkey to violate Syria's territorial integrity, as Ankara continued "inadmissible and provocative" bombings against Syrian territories.
In another development, Russia on Saturday urged the US and other NATO countries to responsibly and carefully choose their targets in Syria.
The comment came as the Serbian foreign ministry earlier confirmed two employees of the Serbian embassy, kidnapped last November in Libya, were killed in the US airstrikes against terror outfit Islamic State (IS).
"This is far from the first time NATO airstrikes have killed innocent people," the Russian foreign ministry said in a statement, expressing deep condolences to the families of the victims.
"Of course, the US and its allies should be guided first and foremost by international law and act not unilaterally, with coordinated steps with all concerned parties in the international community."
The US-led coalition have been conducting airstrikes against terrorist targets in Syria and other Middle East countries since 2014, while Russia started bombing terrorist targets in Syria from last September.
Russia has fallen into "war of words" with western countries on Syrian issues, accusing each other of causing civilian casualties and bombing targets other than terrorists'.
Russian President Vladimir Putin on Saturday claimed that Russian armed forces in Syria "helped Syrian government army and other participants in anti-terror efforts to defeat terrorists, saved civilians from violence, barbarism and tyranny".
"We have always sought to resolve any disputed issues solely through political and diplomatic means, we have repeatedly contributed to stabilizing the situation in different countries, helped resolve serious conflicts," Putin said.
Reiterating that fighting terrorists in Syria is protecting Russia's national interests, Putin said the Russian army must "always be ready to promptly and efficiently respond to any potential threat, to stop any provocation and aggressive actions". (IANS)