Kerry held a first three hours of talks with Russian President Vladimir Putin late Thursday and on Friday was due for a second round with Foreign Minister Sergei Lavrov.
Little filtered out about his Kremlin meeting with the Russian head of state, but Kerry's spokesman said he would "explore initiatives in more detail" with Lavrov.
According to a leaked document seen by the Washington Post, Kerry's key proposal is to offer Russia closer US military cooperation against the Al Nusra Front extremist group, AFP reported.
"The two discussed the need to increase pressure on terrorist groups like Daesh and the al-Qaeda affiliate in Syria, Jabhat al Nusra," US State Department spokesman John Kirby told reporters.
US officials were careful not to call the talks a last chance for diplomacy to resolve the bloody five-year-old conflict, but they warned time is running out.
Moscow and Washington, and the 22-nation contact group they co-chair, have called for a nationwide ceasefire and Geneva-based talks on a "political transition".
A landmark partial ceasefire they brokered in February -- which did not include ISIS or Al-Nusra -- has since all but collapsed amid continued heavy fighting.