In a private conversation during his four-day visit to Canada that ended Wednesday, Charles reportedly compared Hitler's 1939 invasion of Poland with Russia's annexation of Crimea.
In Moscow, Foreign Ministry spokesman Alexander Lukashevich said Russia wanted an explanation from Britain about whether Charles expressed that view and whether the wider British government shares it.
"If these words indeed were said, they don't befit a future British monarch," Lukashevich told reporters Thursday.
"We consider the use of a member of the British Royal Family by the Western press for waging a propaganda campaign against Russia over the pressing international issue — the situation in Ukraine — as unacceptable, outrageous and base," he said.
The Russian Embassy in London in a statement said its officials were meeting British Foreign Office counterparts on Thursday to seek "official clarifications" of the prince's "outrageous remarks."
The controversy comes at a time of heightened tension between Russia and the West. It started after Britain's Daily Mail reported this week that Charles had made the Putin-Hitler comparison Monday during a visit to the Museum of Immigration in Halifax.
The newspaper reported the heir to the throne told Marienne Ferguson, who lost relatives after Germany's invasion of Poland, that Putin was doing just about the same as Hitler. Russia recently annexed Ukraine's Crimea region.
Ferguson later confirmed the content of the comments to the BBC.
Charles's aides have declined to confirm or deny what he said, asserting that they do not comment on private conversations.
Charles's remarks drew criticism from some British politicians, who said the Royal Family should avoid political statements.
However, Prime Minister David Cameron defended Charles on the grounds that everyone was entitled to an opinion. And opposition leader Ed Miliband said Charles "has got a point" in his characterization of Putin.
Charles is scheduled to join leaders of the Second World War Allies, including Putin, at June 6 events in France marking the 70th anniversary of the D-Day landings.
Charles and his wife, Camilla, left Winnipeg on Wednesday to head home after a four-day visit to Canada. Charles said they would cherish their memories of the visit.
--Associated Press reporter Vladimir Isachenkov in Moscow contributed to this report.
--And with files from The Canadian Press