LOS ANGELES — Pinal County, Ariz., Sheriff Paul Babeu — recently and publicly accused of threatening to deport a former boyfriend — denied on Monday that he had done anything illegal and said he would continue his bid for a congressional seat.

“I have never run from a fight and am not going to now,” Babeu told interviewer Wolf Blitzer on CNN.

“I am a single man, never have been married and don’t have a fake girlfriend,” said Babeau, who also served in the military. “I want to be judged on my life of service.”

Last week, the Phoenix New Times, an alternative weekly, reported an allegation that Babeu had threatened to deport his former boyfriend, a Mexican immigrant, if he revealed their relationship. The man was identified only as Jose.

Babeu called the allegation “slanderous and baseless,” though he acknowledged having had a three-year relationship with the man. He said that Jose was a legal resident and that a sheriff didn’t have the authority to deport anyone.

In interviews, Jose has also said that he’s a legal resident.

Babeu said that Jose was an expert on social media and websites and had worked on the sheriff’s campaign as a volunteer. He accused Jose of trying to steal his property, identity and images.

He also noted the timing of the allegations, coming during a difficult race for the Republican nomination for a House seat.

Babeu publicly acknowledged on Saturday that he was gay, and he told CNN on Monday that he supported gay rights — positions that could hurt him in the conservative rural district where he is seeking the nomination.

“I’m not ashamed of who I am,” Babeu said. “Our party is the big tent, the party of Lincoln and of equality.”

In 2008, Babeu defeated a Democrat to become sheriff of Pinal County, south of Phoenix. He has frequently appeared on television to blame the federal government for failing to stop the smuggling of drugs and illegal immigrants across the border. In 2010, Babeu helped Sen. John McCain by campaigning for the Republican’s border security plan.

Last week, Babeu spoke at the Conservative Political Action Conference in Washington, hitting hard at issues that appeal to conservatives — such as the Justice Department’s Operation Fast and Furious investigation into weapons crossing the border.

The furor over the ex-boyfriend’s allegations has led Babeu to quit as a state campaign chairman for GOP presidential contender Mitt Romney. Babeu campaigned with Romney and spoke on robocalls in Iowa attacking Texas Gov. Rick Perry, who has since dropped out of the presidential race.