Sergey Lavrov also was quoted by Russian news agencies as saying Moscow will introduce a resolution in the United Nations on the Ukrainian crisis, but that Russia was not seeking authorization to send in peacekeeping troops. The Ukrainian rebels have suggested that Russia should send peacekeepers, but Moscow says that could only be done with UN authorization.
Ukraine's government and Western countries allege that Russia is fomenting or supporting the uprising in the east, where insurgents have declared two regions independent and are seeking annexation by Russia. Moscow denies it has agents in eastern Ukraine, but it is unclear to what extent it has contacts or influence with the rebels.
Lavrov said that "We know that the rebels in the southeast are ready to hold fire, but the first step by all rights should be made by the Kiev authorities."
He said the proposed UN resolution would concentrate on demanding fulfillment of proposals set forth in a so-called "road map" for resolving the conflict developed by the Organization of Security and Cooperation in Europe.
The OSCE's secretary-general on Thursday visited a camp in Russia for refugees from the conflict in Ukraine's east and called for the fighting to end.
According to the Interfax news agency, Lamberto Zannier said Thursday that the conflict in the east "is craziness which must be stopped."
Russia says some 30,000 people have fled the fighting.
Ukraine's new president, Petro Poroshenko, this week called for establishing safe-passage corridors for civilians who want to escape the violence in the east, but no visible steps toward creating them have been seen.