Kerry was speaking before a meeting with France's foreign minister.
The US blames Russia for recent attacks on Syrian civilians, which Russia denies.
He said: "Last night, the (Syrian) regime attacked yet another hospital and 20 people were killed and 100 people were wounded. Russia, and the regime, owe the world more than an explanation about why they keep hitting hospitals and medical facilities and children and women,"
"These are acts that beg for an appropriate investigation of war crimes and those who commit these would and should be held accountable for these actions."
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