The two generals agreed to maintain their "commitment to de-conflicting" their respective military operations in the war-ravaged country, Dunford spokesman Capt. Greg Hicks said in a brief statement.
Meanwhile, Russian Deputy Foreign Minister Sergei Ryabkov said that Moscow and other countries-guarantors of memorandum have provided the United States with all the information on the document.
Turkey and Iran agreed on Thursday to Russia's proposal for "de-escalation zones" in Syria, a move welcomed by the United Nations but met with skepticism from the United States.
While Russia and Iran support the government of Syrian President Bashar al-Assad, Turkey backs the rebels.
This is the first plan, however, to envisage armed foreign monitors on the ground in Syria. However, it is clear that the Astana agreement is a responsibility.
And a member of the rebel delegation to the talks said on Saturday that the opposition was "recording violations of the deal committed by the regime and its militias".
The details of the plan remain incredibly vague.
He said the largest of the four de-escalation zones covers Idlib province, the northeastern part of Latakia province, the eastern areas of Aleppo province and the northern areas of Hama province.
Russian Federation and Iran appear to be the guarantors of the de-escalation zone agreement.
Al Jazeera's Stefanie Dekker, reporting from Moscow, said the Russian ministry of defence had set out some of the details that would be established next; including making specific maps of the zones, establishing coordinates, and setting up buffer strips and checkpoints which would allow civilians freedom of movement and the access of humanitarian aid.
In the tangled mess that constitutes Syria's battlefields there is much that can go wrong with the plan, which emerged from a summit in Kazakhstan. The Syrian government said it backed the proposal but said it would continue to fight what it called terrorist groups across the country. "As for their actions in the de-escalation zones, now all of them are closed for their flights", reported UPI.
Shelling and gunfire was heard in rebel-held areas of Hama province, with one opposition website reporting an air strike in the area. There was no immediate comment from the Syrian army.
The conflict occurred in the rebel-held village of al-Zalakiyat as fighter jets fired in the Hama countryside, reported the Syrian Observatory for Human Rights.
The safe zone agreement has not been signed by Syrian government officials or the rebel forces fighting them.
The Observatory and the Ghouta Media Center, an activist collective, said a child was wounded when government forces shelled the Damascus suburb of Kfar Batna.
The plan endorsed by Russia, Turkey and Iran calls for a ban on all overflights, but Lavrentyev spoke in response to a question posed by a Russian news agency about US -led coalition aircraft.