Republican Senator Don Ipson said he was "wrong" to make the comment.
He made the remark during a legislative hearing on Tuesday about whether to codify guidelines for police dog teams in the wake of criticism that they were used inappropriately by the state.
He told the state's House of Representatives that they should not "make it restrictive" and that they should "let [police] keep doing their job" during a meeting a meeting of the law enforcement and criminal justice committee.
"We don't want to be restrictive, but I don't have a lot of sympathy, so, and we don't want to harm the public, but if they don't want to get bit, stay home," he said.
His comment was met with fierce opposition. The Alliance for a Better Utah released a statement condemning the senator's remarks.
“It is absolutely appalling that Sen. Ipson would make such a terrible statement in support of police violence,” Lauren Simpson, the alliance’s policy director, said in the statement. “Suggesting that people should just ‘stay home’ if they don’t want to experience police brutality is truly one of the more obscene things to be uttered recently by a sitting lawmaker in Utah.”
Mr Ipson apologised for the comment later on Tuesday.
"It didn't come across the way I meant it, and to the world, I apologize for that, that was wrong," he told local news channel KUTV.
He later attempted to clarify his statements during an interview with The Salt Lake Tribune.
"If you don't want to have a confrontation with a police officer or a K-9 dog ... you don't break the law," he said.
The debate was sparked by an incident in Salt Lake City earlier this year in which a police officer commanded his police dog to bite a black man who was kneeling and had his hands in the air.
The offending officer was charged with a felony after the Salt Lake Tribune published body camera footage of the incident, showing the man complying with police but getting bitten anyway.
“For someone to be laying on the ground and complying and have a dog go after them ... I think was inappropriate,” said Rep. Sandra Hollins, a Democrat, and the Utah legislature's only black member.
Mr Ipson said he has seen the video, and said it was "unfortunate."