NEW YORK — Weeks after the shooting in Tucson, sellers at an Arizona gun show allowed undercover investigators hired by New York City to buy semiautomatic pistols even after they said they probably couldn’t pass a background check, Mayor Michael Bloomberg said Monday.

“After Tucson, you would think that people, particularly at a gun show in Arizona, would have been much more careful in enforcing the law,” he said.

Bloomberg has authorized similar sting operations around the country as part of a push for tougher federal laws to help keep guns off the streets of New York.

But in the sensitive aftermath of the shooting Jan. 8 that killed six people and critically wounded Rep. Gabrielle Giffords, the mayor was questioned about the time and place of his hidden-camera investigation, a $100,000 operation conducted almost clear across the country.

“Let me get this straight: From New York City, they are going to send people to Arizona to look into this?” said state Sen. Ron Gould, a Republican. “They might take a look a little closer to home if they are concerned about guns getting in their state.”

Meanwhile, Democratic Arizona state Sen. Steve Gallardo introduced a bill Monday to require background checks for all sales at gun shows.

The operators of the Phoenix gun show where the investigators made their buys on Jan. 23 issued a statement Monday saying all exhibitors at its shows are required to follow state and federal gun laws.

“Mayor Bloomberg and his ‘task force’ have no legal authority in the state of Arizona, or in any other place in America except New York City,” said the statement from the Crossroads of the West Gun Shows. “These forays into America’s heartland committing blatant acts to entrap otherwise innocent gun owners is an unlawful scheme that is created by Bloomberg’s task force.”

The private investigators, wearing concealed video cameras, were sold the 9 mm guns even after telling two separate sellers they probably couldn’t pass background checks.

While many sellers at gun shows are not required under federal law to perform background checks, it is illegal for them to sell a weapon if they have reason to believe the buyer wouldn’t be able to pass one, the mayor said.