Kerry’s British counterpart, Foreign Secretary William Hague, echoed his sentiments blaming Assad for the talks’ ineffectiveness.
The failure to agree on "an agenda for future rounds of talks ... is a serious setback in the search for peace in Syria, and the responsibility for it lies squarely with the Assad regime," Hague said in a statement.
Both Hague and Kerry were behind an international diplomatic effort last summer to rally support for punitive air strikes against Assad, saying they had evidence showing government forces had used chemical weapons on civilians.
But the push ended in Syria agreeing to dismantle its stockpile in a Russia-brokered plan — although Syria has not met deadlines it committed to for destroying the weapons.
No date was set for a third round of talks and it was unclear whether any would be held, but Kerry said the United States remained committed to the Geneva process and all diplomatic efforts to find a political solution.
Meanwhile, the opposition Supreme Military Council (SNC) on Sunday sacked Salim Idriss, who headed the Western-backed Free Syrian Army (FSA) since Dec. 2012, citing the need for a "restructuring."
The FSA in recent months has been overshadowed by a larger, hardline contingent of rebel forces called the Islamic Front, and both have engaged in infighting with Al-Qaeda-linked extremist fighters who are streaming into Syria.
In December, the SNC defense minister, Asaad Mustafa, told the Daily Telegraph that Idriss, a defected general from the Syrian army, had failed in his post and said, “I don’t think everything can continue in the same way.”
Brigadier Abdullah al-Bashir was appointed in his place, the Council said in a video posted online.
The same day, the leader of the Lebanese armed group Hezbollah, Sheik Hassan Nasrallah, pledged to continue fighting alongside Assad's troops until Sunni Muslim forces fighting with the rebels are defeated.
"We will remain where we should be, our policy hasn't changed," Nasrallah said in a televised speech to commemorate the death of three of the group's leaders, including top military commander Imad Mughniyeh who was killed in a Damascus car bombing in 2008.
Hezbollah fighters have been key to the Syrian army's success on the battlefield since June, when they helped Assad's forces dislodge rebels from the opposition stronghold of Qusair near the border with Lebanon.
"We will be victorious. It's only a matter of time," Nasrallah said.
More than 5,792 people were killed in Syria since the Geneva talks began on Jan. 22, according to activists.
Al Jazeera and wire services
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