PHOENIX -- Mayor Phil Gordon used the U.S. Holocaust Museum shooting in the nation's capital to criticize Sheriff Joe Arpaio for what the mayor characterized as Arpaio's "associations" with neo-Nazis.

"I'm calling upon the sheriff of Maricopa County to denounce the neo-Nazis and the Nazi's today," Gordon said at a news briefing on Wednesday.

• Watch: Arpaio: 'I Don't Support Neo-Nazis'

Gordon made it a point to say he did not believe Arpaio is a Nazi or neo-Nazi. Published reports, photographs and YouTube videos showing the sheriff with known Neo-Nazi or white supremacists prompted the mayor's comments.

"He has given the sense of recognition to the Neo-Nazis and Nazi's that he's associated with and he's known that these are Neo-Nazis and Nazi's," Gordon said. "I ask the sheriff today to publicly disavow his associations with these hate-mongers and apologize."

Arpaio said he was saddened by the mayor's remarks.

"I don't support any neo-Nazi or racist organization," Arpaio said at a late-afternoon news briefing. “That’s a pretty low blow that he did to me.”

One of the examples that Gordon cited was a photograph of Arpaio with Tom Coletto, a known Neo-Nazi. The photograph was taken at a protest in May.

According to the sheriff, he did not know who Coletto was when he took the picture. Coletto, in an interview with CBS 5 News, agreed that the sheriff was unaware of his ties to Neo-Nazis when the picture was taken.

Coletto, who has since renounced his ties to the group, did say that many Neo-Nazis and white supremacists admire the sheriff.

“He is a rallying point for white nationalists and Neo Nazis,” Coletto said.

An elderly gunman, said by authorities to have a violent and virulently anti-Semitic past, stepped inside the crowded museum on Wednesday, opened fire with a rifle and fatally wounded a security guard before being shot by other officers.

Law enforcement officials said James Von Brunn, 88, a white supremacist, was under investigation in the museum shooting, and a second official said the elderly man's car was found near the museum and tested for explosives.