"No," Peskov told reporters when asked whether he could confirm that there had been such a warning.
On Saturday, media reported citing sources that Bolton told Patrushev at the Thursday talks in Geneva that the United States was ready to take military action if Damascus used chemical weapons in the Idlib province.
Earlier in the day, Russia's Deputy Foreign Minister Sergei Rybkov said that Bolton's statements on Syria and threats were likely to be the only language that the US has used.
Kremlin spokesman also noted that Russia's expenditures on its defense capacity, including during the Vostok 2018 military exercises, are justified in the current international situation.
"The country's defense capability in the current international situation, which is often very aggressive and unfriendly toward our country, is justified, necessary and has no alternative," Peskov told reporters when asked about Russia's expenditures on the Vostok drills.
Russia, alongside Iran and Turkey, is a guarantor of the ceasefire regime in Syria. Moscow has also been assisting Damascus both through supporting the struggle against terrorist groups and providing humanitarian aid to the residents of the crisis-torn country.
Syria has been devastated by years of violent military conflict which with government forces fighting multiple militant and terror groups.