"The carefree attitude of youth may be an explanation but it can't in any way serve as an excuse and especially not as justification," Mr Roux told reporters in Montreal after meeting Jewish leaders. "I committed a mistake by yielding to the anti-Semitic feelings that poisoned our minds at the time."
The Jewish leaders accepted his apology and said he done the honorable thing in resigning on Tuesday.
Mr Roux, a prominent actor who was appointed the province's lieutenant- governor in September, also admitted in a magazine interview that he participated in a 1942 anti-conscription protest that degenerated into vandalism against Jewish shops.
Mr Roux's comments angered Jewish groups and provided ammunition for Quebec's separatist leaders, who had bitterly opposed his appointment as lieutenant governor by the Prime Minister, Jean Chretien. Mr Roux, like Mr Chretien, is an outspoken federalist who wants Quebec to remain in Canada.
Lieutenant-governors are the Queen's representatives in Canadian provinces, although they are in effect named by the national government. The posts are mostly ceremonial, and they are supposed to stay out of partisan politics.
Mr Roux, 73, had said on Monday his actions were youthful bravado and not an indication of support for the Nazis. He expressed regret for any offence.
Fascist and anti-Semitic sentiment was not uncommon in Quebec. Some members of Quebec's francophone majority initially were more sympathetic to the collaborationist Vichy regime in France than to the Allies.
Mr Chretien said on Tuesday in Parliament that he was unaware of Mr Roux's past when making the appointment. "The whole life of Jean-Louis Roux was, in my view, an impeccable record, except for one mistake," the Prime Minister said.
"He made a mistake when he was 19 years old. Nobody can take away his great career and his great service to the Canadian people, and the people of Quebec in particular."
Mr Roux said he drew a swastika on the sleeve of his laboratory coat as a pre-medical student in Montreal. "This display, which unfortunately testifies to the attitude of a large portion of the youth in Quebec at the time, was inspired only by a medical student's mischievous desire to show off and to be provocative, and in no way corresponded to any political conviction or ideology on my part," he added.
Mr Roux said that while he participated in the anti-conscription demonstration, he was not among those who smashed windows of Jewish shops.
Quebec's separatist Prime Minister, Lucien Bouchard, took advantage of Mr Roux's downfall to push for the eradication of his post."It's really time to get rid of that archaic function which is a remnant of our colonial past," he said.