Peskov said that Russian President Vladimir Putin had urged people in Ukraine to lay down their weapons, adding that it will prevent possible clashes, Sputnik reported.
The warning from the Kremlin comes in response to steps by Kiev, as the Ukrainian government has handed out military weapons to civilians.
On February 24, Russia launched what it called "a special military operation" in Ukraine to "protect civilians in the Donbass People's Republics.
Putin said the key goal of the operation is the "demilitarization and denazification" of Ukraine, adding that Moscow aims to eliminate a threat to Russia's national security.