Via his Twitter feed, Zuroff said he was "utterly disgusted" by the prospect of Cukurs being portrayed onstage in a sympathetic light.
Utterly disgusted by attempts to whitewash crimes of Latvian deputy commander of Arajs death squad Herbert's Cukurs!!!— Efraim Zuroff (@EZuroff) October 7, 2014
Writing on the i24 news website, Zuroff condemned the musical which is due to premiere in Liepaja on Saturday 11 October as "a brazen attempt to rehabilitate the image of one of the most notorious mass murderers of Jews in the Baltics during the Holocaust."
Zuroff, who is a familiar figure in Latvia as he annually bears witness to the unofficial March 16 commemoration of the Latvian Legion, divisions of the Waffen-SS, said the play was part of a "campaign to restore him to national glory in Latvia."
For his part, Zuroff is in no doubt about Cukurs' active role in the holocaust and his opinion piece cites numerous disturbing examples of Cukurs' alleged crimes based on the testimony of holocaust survivors.
Cukurs became a famous aviator in the 1930s and was acclaimed a national hero after flying from Riga to the Gambia in Africa in a self-built airplane.
However, during the second world war he became an officer in the notorious 'Arajs Kommando', a pro-Nazi local militia that participated enthusiastically in the slaughter of Latvia's Jewish population.
After the war Cukurs went on the run, so was never put on trial.
Israel's Mossad intelligence agency finally tracked him down in Uruguay in 1965 and summarily executed him.
The project itself has not been without problems. Original lyricist Andra Manfelde withdrew from the project in May claiming she had known Cukurs only as an aviator and not as someone linked to Nazi war crimes.
"In today's Latvia, for far too many Latvians, it is Cukurs who earns their sympathy, while his Jewish victims are forgotten, or even worse, erased from the historical record," Zuroff said.