Bloomberg's office didn't bother to give Arizona police any advanced notice of the plan, Attorney General Tom Horne said.
"The fact that no such notification was made indicates this so-called sting is nothing less than a public relations stunt," Horne said.
During the sting disclosed Monday by Bloomberg, investigators hired by New York City bought semiautomatic pistols after they said they probably couldn't pass a background check.
Bloomberg has authorized similar stings around the country as part of a push for tougher federal laws to help keep guns off the streets of New York.
Horne said Bloomberg ought to consider the skyrocketing crime in his city before sending police officers to another state. He cited the latest FBI crime statistics that show robberies, rapes, aggravated assaults and murders increased in New York City in 2010, compared to the previous year.
Bloomberg spokesman Jason Post said the sting was carried out by Arizona-based private investigators, not New York City police.
"According to data contained in FBI reports, New York City is the safest big city in the nation, safer than Phoenix," where the per capita rate of major felonies is twice that in New York, Post said.
Investigators who ran the sting were sold 9 mm guns even after telling two separate sellers they probably couldn't pass background checks.
The mayor has said it's illegal for merchants to sell a weapon if they have reason to believe the buyer couldn't pass a background check, even though many aren't required to perform such checks.
The mayor conceded that most illegal guns in New York City are coming from states along the East Coast.