Ramzan Kadyrov, a close ally of Russian President Vladimir Putin, made the comments after France warned its citizens living or traveling in several Muslim-majority countries to take extra security precautions because of anger over the cartoons.
The row has its roots in a knife attack outside a French school on Oct. 16 in which a man of Chechen origin beheaded Samuel Paty, a teacher who had shown pupils cartoons of Prophet Mohammad in a lesson on freedom of speech.
The caricatures, first published by a satirical magazine whose Paris offices were attacked by gunmen killing 12 people in 2015, are considered blasphemous by many Muslims.
Kadyrov, an ex-rebel who endorsed a Kremlin military campaign that crushed an Islamist insurgency in Chechnya and nearby Russian regions, has played down the fact that Paty's attacker was born in Chechnya, saying he grew up in France.
In an Instagram post on Tuesday, Kadyrov said Macron was wrong to characterize the display of such cartoons as free speech.
"You are forcing people into terrorism, pushing people towards it, not leaving them any choice, creating the conditions for the growth of extremism in young people's heads. You can boldly call yourself the leader and inspiration of terrorism in your country," Kadyrov wrote, addressing Macron.Macron, who hailed Paty as "a quiet hero," has pledged to fight "Islamist separatism."