The Index.hr portal uploaded the video with the headline "Stipe Mesic's Pro-Ustasha Speech".
Mesic's office said in a statement that it refused to comment, recalling the president's positions on the Ustasha ideology.
"We particularly point to his statements at the site of the former concentration camp Jasenovac," read the statement, underlining that those statements "are the only response to the malevolent attempt to take several sentences out of the context they were said in".
In the video, aired by Croatian Television on Saturday evening as well, President Mesic speaks in a positive light of the Independent State of Croatia (NDH, 1941-45).
"You see, in the Second World War, the Croats won twice and we have no reason to apologise to anyone. What they ask of the Croats the whole time, 'Go kneel in Jasenovac, kneel here...' We don't have to kneel in front of anyone for anything! We won twice and all the others only once. We won on April 10 when the Axis Powers recognised Croatia as a state and we won because we sat after the war, again with the winners, at the winning table," Index.hr quoted Mesic as saying.
The portal requested several politicians for comment, including Zarko Puhovski, president of the Croatian Helsinki Committee on Human Rights, saying it did not reveal the identity of the person who glorified the Ustasha ideology.
"In the early 1990s many politicians and public figures used the Ustasha ideology, thinking that they would achieve something good," said Puhovski.
The leader of the Democratic Centre party, Vesna Skare-Ozbolt, vehemently condemned the speech. "This is a totally sick speech. The speaker is certainly not thinking of the modern Croatian state and is creating an unnecessary mortgage. It sounds like the speech of a radical right winger."
The leader of the Social Democrats, Ivica Racan, said that any use of the Ustasha ideology should be condemned, regardless of when it was used, but recalled that in the early 1990s the Ustasha ideology was used much more than today.
Index.hr quoted him as saying that since this was an old case, "we should first see in what context what we see in the video was said".
The president of the Serb National Council, Milorad Pupovac, was quoted as saying that the speech was a typical example of (ex-Croatian President Franjo) Tudjman-speak and that if the recording was authentic, (the speaker in the video) should admit his error.
Social Liberal vice president Ivan Cehok was quoted as saying that any referring to the NDH was "a total political flop".