The picture titled 'The Virgin of the Third Reich' is just one of many paintings featuring famous figures including Jesus Christ and Pope Benedict XVI.
Veneziano's art has stoked controversy in the Catholic and Jewish world with many calling them offensive.
Pietrasanta father Stefano D'Atri has demanded the mayor cancel the exhibition.
He said: "That painting offends us as faithful and as people who lived during the terrible period of Nazism. We don't hide behind art."
Lord Mayor Domenico Lombardi said: "I take full responsibility for this problem. I'd never seen it before I approved it otherwise I would have chose another painter for this exhibition slot.
But the artist defended his work, he said: "If art cannot provoke, what can it do?"
SIC: TCUK