Putin told US talk-show host Tucker Carlson last week that Russia was ready for "dialogue."
Lavrov alluded to any world leaders who did not take Putin's "acts of goodwill" seriously enough may regret their lack of allegiance.
CIA hopes to recruit Russians disaffected by Ukraine war
Ukraine has recently stepped up attacks on Russian targets in and around Crimea.
The assault follows Russia's largest air attack on Ukraine on Friday which killed at least 39 people.
Artyoom Reznik's home Jewish community in the city of Kharkiv mourned his loss.
"I don't want to boast, but I can say that we began to gain and picked up the pace of production earlier than Western countries," a minister handling weapon production said.
Russia has previously reported a number of incidents in which its fighter jets were scrambled to intercept military planes from Norway, another NATO member, over the Barents Sea.
"These morons are actively pushing us towards World War Three," Medvedev said.
After it invaded Ukraine last year, Moscow closed off the Black Sea ports of one of the world's biggest suppliers of grain.
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