Brahimi acknowledged the high stakes. He told Kerry and Lavov that their chemical weapons negotiation "is extremely important in itself and for itself, but it is also extremely important for us who are working with you on trying to bring together the Geneva conference successfully."
More than 100,000 people have been killed in two years of civil war. On Friday the international group Human Rights Watch accused the Syrian government and militias fighting on its side of carrying out summary executions that killed at least 248 people in two towns in May.
Kerry, flanked by Lavrov and Brahimi, told reporters after an hourlong meeting that the chances for a second peace conference in Geneva will require success first with the chemical weapons talks, which have been "constructive" so far.
"I will say on behalf of the United States that President (Barack) Obama is deeply committed to a negotiated solution with respect to Syria, and we know that Russia is likewise. We are working hard to find the common ground to be able to make that happen," Kerry said.
"We discussed some of the homework that we both need to do," he added.
Kerry said they agreed to meet around Sept. 28 on the sidelines of the annual U.N. General Assembly high-level meetings in New York.
But, he said, the future of peace negotiations depends on the outcome of the weapons talks.
"We are committed to try to work together, beginning with this initiative on the chemical weapons, in hopes that those efforts could pay off and bring peace and stability to a war-torn part of the world," he added.
Brahimi also met privately with Kerry at a Geneva hotel on Thursday to explore ways to resume international negotiations last held in Geneva in June 2012 aimed at ending the Syrian civil war.
Lavrov said Russia has supported the peace process from the start of the Syrian conflict and said he had discussed with Kerry and Brahimi the Geneva communique from the 2012 meeting on Syria and ways of preparing for a second conference.
"It is very unfortunate that for a long period the Geneva communique was basically abandoned," said Lavrov.
He said that document "means that the Syrian parties must reach mutual consent on the transitional governing organ, which would come with full executive authority. And the communique also says that all groups of Syrian society must be represented."
When the chemical weapons talks began Thursday, Kerry bluntly rejected a Syrian pledge to begin a "standard process" by turning over information rather than weapons — and nothing immediately. The American diplomat said that was not acceptable.
"The words of the Syrian regime, in our judgment, are simply not enough," Kerry declared as he stood beside Lavrov. "This is not a game."
Salem Al Meslet, a senior member of the opposition Syrian National Coalition, said he was disappointed that the Kerry and Lavrov meeting on chemical weapons wasn't about punishing Assad.