MOSCOW—The Western-led military action in Libya provoked a rare public split in Russia's ruling tandem Monday, as President Dmitry Medvedev appeared to scold his patron, Prime Minister Vladimir Putin, for publicly criticizing the effort.

Dressed in a fur-trimmed leather bomber jacket embroidered with the words "Commander in Chief" in Russian, Mr. Medvedev defended his decision not to veto the United Nations Security Council resolution authorizing the action and warned critics to watch their words.

"It's...