Kerry says Syria's government is not supposed to bomb the opposition under the truce that went into effect Monday.
But Kerry says Assad will be able to go after the al-Qaeda-linked Nusra Front in certain areas.
After seven days of calm, the US and Russia would then cooperate on how to combat Nusra, the Associated Press reported.
But Kerry said Monday that Assad would still be allowed to target Nusra after that point if strikes "are agreed upon with Russia and the United States."
The US had not previously spoken about approving Syrian government attacks.