New York (CNN) -- Undercover investigators purchased semiautomatic weapons at an Arizona gun show, despite telling vendors that they probably could not pass background checks, New York Mayor Michael Bloomberg told reporters Monday.

"We have demonstrated how easy it is for anyone to buy a semiautomatic handgun and a high capacity magazine, no questions asked," Bloomberg said.

The investigation followed the recent shooting in Tucson, Arizona, that left six people dead and injured 13 others.

The mayor presented undercover video showing the sales, including illegal firearms sales at a gun show in Phoenix, Arizona.

Bloomberg called on lawmakers to enact stricter gun control and to close the so-called "gun show loophole" that permits buyers to purchase weapons from private "occasional" sellers without background checks.

Gun advocates say the law specifically exempts people who only occasionally sell guns at gun shows, which they say cannot be considered a "loophole."

Last week, Bloomberg joined the eldest son of slain civil rights leader Martin Luther King Jr. in an effort to persuade President Barack Obama to raise the issue of tighter gun control during his State of the Union address.

Obama did not.

"I thought that he missed an opportunity," Bloomberg told reporters. "But I was encouraged that some members of his staff said that he is going to take it up separately."

The mayor has remained outspoken on gun control, noting the more than 400,000 people killed as a result of gun violence since 1968 when King and Robert F. Kennedy were slain by assassins' bullets.

The ease of access to high-powered firearms in U.S. border states, like Arizona, may also play a hand in fueling Mexican drug violence, according to a 2009 U.S. Government Accountability Office report.

"While it is impossible to know how many firearms are illegally smuggled into Mexico in a given year, about 87 percent of firearms seized by Mexican authorities and traced in the last 5 years originated in the United States," the report said.

Many of these firearms come from gun shops and gun shows in Southwest border states, it added.