Speaking after talks with UN envoy Staffan de Mistura, Kerry said he would call his Russian counterpart Sergei Lavrov later Monday to press for the ceasefire to be restored.
But, in some of his most downbeat comments yet on the effort to end the deadly five-year-old conflict, Kerry warned that he did not want to promise success.
Standing by de Mistura, he thanked him for supporting a political process in the midst of "a conflict that is in may ways out of control and deeply disturbing to everybody in the world, I hope."
There, he said, Bashar al-Assad's regime had deliberately targeted three clinics and a major hospital, killing doctors and patients and threatening the truce.
"The attack on this hospital is unconscionable," he said. "And it has to stop.