The two powers back opposing sides in the conflict, with Moscow supporting the Syrian government President Bashar al-Assad and Washington backing a coalition of militia it regards as “moderate rebels”.
A leading member of the “High Negotiations Committee” said the opposition umbrella group cautiously welcomed the agreement.
"We welcome the deal if it is going to be enforced," said Bassma Kodmani.
Syrian ceasefire came after marathon talks between Lavrov and Kerry in Geneva late on Friday.
Both Kerry and Lavrov said the complex plan is the best available chance to end fighting between the government and mainstream rebels while still targeting terrorists from former Al-Qaeda affiliate Al-Nusra Front or by its new name Fatah Al Sham and the Islamic State (ISIS, ISIL, IS and Daesh) group.
The question of Assad's fate remains, with Western powers calling for his ouster and Russia backing him.
Key to the deal is the delivery of desperately needed aid to civilians in rebel-held areas of Syria's second city Aleppo which are under siege by Army forces.
Russia also needs to persuade the Syrian air force to stop strikes on rebel-held Positions and in turn, Washington must get opposition groups it backs to separate themselves from the former Al-Nusra, now called Fateh al-Sham Front, which has allied itself with a range of rebels at different points in the fluid conflict.
Kodmani said the rebels would break ranks with the “jihadists” if the truce deal held.
"The moderate groups will reorganize and distance themselves from the radical groups. We will do our part," she said.
Charles Lister of the Middle East Institute said mainstream rebels view the US-Russia talks with extreme distrust and seem reluctant to disassociate themselves from the powerful “jihadists” in case the ceasefire fails.
Rebels now face the "biggest and most momentous decision since they chose to take up arms against the government Army in 2011," he said.
Turkey and British Foreign Minister Boris Johnson welcomed the deal.
UN Syria envoy Staffan de Mistura said that the deal provided a "window of opportunity" and that he would begin consultations on a relaunch of peace talks.
German Foreign Minister Frank-Walter Steinmeier said: "Everything now depends on rapid implementation."
The Syria truce deal follows heavy fighting around Aleppo in recent weeks in which the rebels fought unsuccessfully to break the government siege.
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