PHOENIX -- Sheriff Joe Arpaio and Phoenix city leaders continue to trade barbs over enforcement of immigration laws in the city.

Arpaio wrote an angry letter to City Manager Frank Fairbanks on Monday, accusing Phoenix Police Chief Jack Harris of trying to strip the sheriff of his power to arrest illegal immigrants and accusing Mayor Phil Gordon of "negative and misleading rhetoric" in discussing the sheriff's actions and motives.

Arpaio's letter came after Harris contacted federal officials about Arpaio's relationship with the Immigration and Customs Enforcement agency.

"If the police chief thinks, when he called federal officials hoping to go to Washington to curtail the authority I have -- 160 officers to enforce the federal immigration laws -- I've got news for him," Arpaio declared.

Gordon denied the city is trying to curb the sheriff's ability to work with ICE.

"It was not to revoke ICE, but to look at it to see what could be done to protect our officers and his officers," the mayor said.

Gordon said he just wants the two agencies to work together when it comes to taking criminals off the street. He asked that the sheriff provide more notice to police when sending his officers to city locations.

"All we have been asking for is for the sheriff to act professionally and not only to notify, but to work quietly with the police department so as not to endanger any officers, local or federal," Gordon said.

Arpaio said he gives plenty of notice and has written proof that his commanders notified Phoenix police "days" before two recent patrols in areas that cater to day laborers. Those patrols have become the catalyst for the fight between the two agencies.

Arpaio wrote Fairbanks, "For this mayor and the chief of police to try to destroy my fight against illegal immigration because they don't want me to do it, I got news for them. We're going to keep doing it."

Gordon said there are thousands of felony warrants for hard-core criminals sitting on the sheriff's desk and that he is focusing instead on arresting illegal immigrants for traffic violations.

"I believe the sheriff should be using his ICE authority to go after those in this country illegally who are committing crimes," Gordon said, adding that he means serious crimes like murder, robbery, drugs and human smuggling, not traffic violations.

In his letter to Fairbanks, Arpaio said Gordon is making "public and inflammatory remarks which may, in fact, cause civil disobedience in his community."

He said that hours before the sheriff's office began an operation near Cave Creek and Bell roads last Friday, Gordon spoke at a Cesar Chavez luncheon "and claimed a neo-Nazi was behind the business people's request there and that the Sheriff's Office only locks up brown-skinned people with broken tail lights. He ended his speech by calling on everyone to speak out against me and my deputies and make their voices heard."

Arpaio said those statements created a larger, angrier protest group and resulted in a hostile environment.