Kerry said the cessation of hostilities would not apply to Islamic State and other militant groups fighting in Syria, he added. Islamic State militants control large parts of Syria and Iraq.
Russian Foreign Minister Sergei Lavrov told the news conference that Russia would not stop air attacks in Syria, saying the cessation of hostilities did not apply to Islamic State and al Nusrah, which is affiliated with al Qaeda.
The United States and European allies say few Russian strikes have targeted those groups, with the vast majority hitting Western-backed opposition groups.
Lavrov said peace talks should resume in Geneva as soon as possible and that all Syrian opposition groups should participate. He added that halting hostilities would be a difficult task.
But British Foreign Secretary Philip Hammond said ending fighting could only succeed if Russia stopped air strikes supporting Syrian government forces' advance against the opposition.
It cautioned, however, that the agreement must prove to be effective before it joins political talks with government representatives in Geneva.