Croatian President Kolinda Grabar-Kitarovic's office shrugged off the incident, insisting there was "nothing questionable" about it.
The photo, posted on Facebook by a Croatian man living in Canada, shows Grabar-Kitarovic posing with him and others in front of a flag bearing the coat of arms used by Croatia's World War II-era Ustasha regime, which persecuted and killed hundreds of thousands of Serbs, Jews, Roma and anti-fascists.
The checkerboard-patterned shield in the middle of Croatia's current national flag has 25 red and white squares, starting with a red one in the top-left corner.
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A different version with a white square in that corner has been used at other points in Croatia's history - notably by the Ustasha. It was replaced by the current shield after World War II when Croatia was part of the former Yugoslavia.
Both versions were briefly in use in 1990 ahead of Croatia's declaration of independence, but under a December 1990 law the national flag bears the red-first version of the shield.
The presidency batted off the row over the photo of Grabar-Kitarovic, telling N1 television, "We see nothing questionable in it." It noted that such a flag was displayed in front of the Croatian parliament in 1990.
The president's view on the wartime regime is "clear and she voiced it on several occasions," it added. Grabar-Kitarovic has condemned the Ustasha in the past.
The row sparked mixed responses online.
"This issue involving our president is more than shameful," Visnja Skreblin, a woman from Zagreb, commented on online portal Index.
But reader Mario Babic defended the president, saying it was "Croatia's historic shield, created far before the darkest chapter of Croatia's history."
Grabar-Kitarovic took over the presidency - a role with limited powers - in 2015 as the candidate of the ruling conservative HDZ party.
The previous HDZ-led government, which fell in June, was accused by critics of turning a blind eye to a far-right surge in the country, including nostalgia for the pro-Nazi past.
