US Secretary of State John Kerry says all alleged violations of the partial truce in Syria will be investigated.
He said the US and Russia were working on a mechanism to ensure air strikes only targeted so-called Islamic State (IS) or al-Qaeda-linked al-Nusra Front.
Mr Kerry said they had agreed not to debate alleged violations in public.
On Monday, aid convoys began reaching besieged areas of Syria as the cessation of violence, which began on Saturday, appeared to be holding.
But France expressed concern about reports of strikes by Syrian government and Russian aircraft on areas controlled by mainstream rebels.
Russia says it is only targeting UN-designated terrorist organisations - including IS and al-Nusra, which is part of a major rebel alliance - in line with the terms of the cessation of hostilities.