PHOENIX -- The war of words between Phoenix Mayor Phil Gordon and Maricopa County Sheriff Joe Arpaio has reached new heights.

"I want to send a message to him right now - you put up or you shut up," Arpaio said.

Arpaio is upset with what he call lies from the mayor about the sheriff's work performance.

"You are making all these allegations with no basis including your request for the Justice Department to investigate me based on news articles," Arpaio said.

Apaio told News/Talk 92.3 KTAR's Darrell Ankarlo he wonders why the mayor doesn't have the guts to face him in person with his accusations that the sheriff is going after brown skin and broken tail lights instead of real felons.

Earlier Thursday, Gordon told Ankarlo the sheriff should worry about the dangerous fugitives in Maricopa County rather than doing immigration roundups.

"You don't want to go after 37,500 violent illegal criminals and criminals, fine. Go after the 1,500 that he himself was saying I'm responsible for, before you go and spend all that money and resources going after broken tail lights," Gordon said.

The sheriff calls the mayor's words a bunch of garbage.

"We are in the black. He ought to look at his city and see how many million and millions he's in the red," Arpaio said. "Maybe he should be worried about that."

In response to the sheriff's office offering to let Phoenix Police take over policing the town of Guadalupe, Gordon said this to KTAR's Ankarlo.

"If he's willing to give up jurisdiction in Guadalupe, let me suggest, why doesn't he let Phoenix then manage Phoenix's problems," Gordon said.

In other words, sheriff, the mayor wants you to focus on the unincorporated areas of the county.

"So that will never happen in a billion years. They just want to get rid of this sheriff. They're throwing hype in there," Arpaio said.

The mayor told Ankarlo the feud is not about illegal immigration, it's about professional consideration.

"Don't make this an illegal immigration debate to try to hide the fact that the sheriff is taking resources, going into cities and not coordinating with the professionals," Gordon said.

Arpaio said he has documentation showing he's coordinated his roundups with city police. He says the mayor's public allegations against him are garbage.

"He has no power, except his tongue and talking," Arpaio said.

And, the sheriff says Gordon ought to talk to him personally about any issues he has rather than use platforms like the state of the city address to attack him.

"I can see him from my window," Arpaio said. "He has never called. His chief of police has never called. So, we know, what's his problem? Is he afraid to face me face to face?" Arpaio said.