The Prince of Wales' alleged remark about Mr Putin's actions over Ukraine reportedly came during a four-day tour of Canada when he spoke to a woman who fled the Nazis and lost family members in the Holocaust.
A spokesman for Clarence House said: "We do not comment on private conversations.
"But we would like to stress that the Prince of Wales would not seek to make a public political statement during a private conversation."
Charles was being shown around the Museum of Immigration in Halifax, Nova Scotia, along with Camilla, the Duchess of Cornwall.
The pair paid tribute to World War Two veterans and their families, and during the course of the visit they spoke to museum volunteer Marienne Ferguson.
Ms Ferguson told the Prince she fled to Canada with her family in 1939, not long before Hitler annexed the Baltic coastal Free City of Gdansk.
Speaking to the Press Association after meeting Charles, the 78-year-old said: "The Prince said, 'And now Putin is doing just about the same as Hitler'.
"I must say that I agree with him and am sure a lot of people do.
"But I was very surprised that he made the comment as I know they (members of the Royal Family) aren't meant to say these things.
"I told the Prince that while my family and I were lucky to get a permit to travel, many members of my relatives had permits but were unable to get out before the war broke out on September 1.
"They were sent to the concentration camps and died."
UK Labour (Co-op) MP Mike Gapes, who represents Ilford South, has condemned the comments.
He said on Twitter: "If Prince Charles wants to make controversial statements on national or international issues he should abdicate and stand for election.
"In constitutional monarchy policy and diplomacy should be conducted by parliament and government. Monarchy should be seen and not heard."
Charles and the Russian leader are due to meet next month when they attend the 70th anniversary of the D-Day landings in Normandy on June 6.
Mr Putin has faced international anger over Russia's actions in neighbouring Ukraine, including the controversial annexation of Crimea.
