"The regime stonewalled. They did nothing except continue to drop barrel bombs on their own people and continue to destroy their own country. And I regret to say they are doing so with increased support from Iran, from Hezbollah and from Russia," he said in Jakarta during a trip to Asia and the Middle East.
Pressing Moscow to wring a more flexible stance from Assad, he said: "Russia needs to be a part of the solution", rather than helping the Syrian leader with arms and other support.
In Moscow, Russian Foreign Minister Sergei Lavrov hit back, citing "evidence that certain sponsors of the opposition are starting to create a new structure" bringing in Assad foes who have left the main opposition National Coalition.
"In other words, a course is being set to move away from the negotiations track and once again place bets on a military scenario," Lavrov said at a joint news conference after talks with his Eritrean counterpart.
He also faulted the United States for failing to ensure the presence of a broadly representative opposition delegation at the Geneva talks, saying that Russia had done its part in getting Assad's government to the table.
"Russia is always being urged to make more of an effort to resolve the Syrian conflict," Lavrov said. "When we hear that Russia must take some steps, it's necessary to remember one simple truth: We have done everything we promised."
Moscow helped Syrian government negotiators resist discussion of a transitional governing body for Syria at the Geneva talks last week by suggesting it endorsed their demands that tackling "terrorism" top the agenda.
The Syrian government's efforts to make that a priority were "completely justified" because Syria "is increasingly becoming a magnet for jihadists and Islamic radicals of all stripes," the Russian Foreign Ministry said on Monday.
Russia has accused sponsors of the rebels of pushing for "regime change".
The conflict has drawn thousands of foreign fighters into Syria to fight either for the mostly Sunni Muslim rebels or for Assad, whose Alawite sect is an offshoot of Shi'ite Islam.
Kerry derided the Syrian government's insistence that terrorism should be the main focus of the Geneva peace talks.
"Assad himself is a magnet for terrorists," he said, accusing him of pursuing "state-sanctioned terror against his own people" by indiscriminate bombing, starvation and torture.