"If Assad does not adhere to this, there will clearly be repercussions and one of them may be the total destruction of the ceasefire and they go back to war," Kerry said.
Read more from our special coverage on "SYRIA"
"I don't think that Russia wants that. I don't think that Assad is going to benefit from that," he said.
"There may be even other repercussions that are being discussed but that is for the future to determine."
A February 27 truce between the Syrian regime and non-jihadist rebels raised hopes for efforts to resolve the five-year conflict.
But it has all but collapsed amid renewed fighting, the worst of it in Aleppo where a surge in violence has claimed more than 270 lives since April 22.
Washington and Moscow are now working together to include Aleppo in a freeze in fighting aimed at bolstering the broader truce brokered by both world powers.
"The cessation of hostilities was put in place precisely to give the people on the ground who are innocently caught between these warring factions some breather, some ability to be able to be safe and work this out at the negotiating table," Kerry said.
"That is why we are working urgently right now to reaffirm the cessation of hostilities nationwide."
Russia said today it hoped a new ceasefire could be announced within hours for Aleppo.
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