The lighthearted-yet-menacing intervention came alongside more forthright comments from spokeswoman Maria Zakharova, who called the PM's words "irresponsible and unfounded".
She said that a pledge to uphold the international order sounds particularly "cynical" given British action in Iraq and Libya that "caused suffering of millions and destabilised entire regions".
Ms Zakharova argued that Britain is facing hard times following its decision to leave the European Union, adding that " Russia has been chosen as a foreign enemy needed to deflect public attention".
Ms May had said: "In a recent speech President Putin said that while the interests of states do not always coincide, strategic gains cannot be made at the expense of others.
"When a state fails to observe universal rules of conduct and pursues its interests at any cost, it will provoke resistance and disputes will become unpredictable and dangerous.
"I say to President Putin, I agree. But it is Russia’s actions which threaten the international order on which we all depend."
The Kremlin "will not succeed" in destabilising the democratic nations, she added.
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