The Daily Mail says Charles made the comment during a visit Monday to the Canadian Museum of Immigration in Halifax.
The newspaper reports museum volunteer Marienne Ferguson as saying her Jewish family fled to Canada from Poland when she was 13, but that other relatives failed to flee before the German army arrived in Gdansk in 1939.
It quotes Ferguson as saying she told Charles about her family background and how she came to Canada, and that Charles then said to her: "And now Putin is doing just about the same as Hitler."
The Canadian Press could not immediately reach Ferguson for comment about the report.
A spokeswoman for Clarence House, the residence of Prince Charles, told the news agency early Wednesday, ‘‘We don‘t comment on private conversations.‘‘
‘‘We do like to stress that the Prince of Wales wouldn’t seek to make a political statement during a private conversation,‘‘ the spokeswoman added.
Ferguson later told the BBC it was "just a little remark. I didn't think it was going to make such a big uproar."
Tensions have grown between Putin and the West since Russia's annexation of Crimea earlier this year.
Charles is scheduled to wrap up his trip to Canada on Wednesday in Winnipeg.
But his reported comments have caused a media storm in Britain, where Charles has sometimes been accused of compromising the Royal Family's political neutrality with his strong views on topics including education, architecture and the environment.
Labour party legislator Mike Gapes tweeted that in a constitutional democracy, "monarchy should be seen and not heard."
But Deputy Prime Minister Nick Clegg said the prince was "free to express himself."
"I have never been of this view that if you are a member of the Royal Family somehow you have to enter into some Trappist vow of silence," Clegg told the BBC.
Officials in Moscow had no comment.
On June 6 Charles is due to join his mother the Queen and leaders of the Second World War Allies — including Putin — at events in France to mark the 70th anniversary of the D-Day landings.
— With files from the Associated Press
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