The nation's top National Guardsman has invited New York Mayor Ed Koch to visit Utah's West Desert to see that military summer camp is tough enough without adding drug searches to the job.

"I believe the distinguished mayor would be pleasantly surprised at what, in reality, guardsmen do at annual training, should he view some of that training firsthand," Maj. Gen. John Matthews said.Matthews, adjutant general of the Utah National Guard and president of the Adjutants General of the United States, was responding to Koch's anti-drug speech earlier this week to the U.S. Conference of Mayors' convention in Salt Lake City.

Koch urged the use of guardsmen and Army reservists, during annual summer training, to search for drug shipments in all cargo entering the United States.

The New York mayor said that would be better than summer training camps where he claimed reservists and guardsmen are "sitting on their butts."

Matthews says Koch "left the impression it was general knowledge that National Guardsmen go to annual training for two weeks each year and sit around" and are not already helping stem the flow of illegal drug shipments.

He invited Koch to attend FIREX '88, through June 26 in western Utah. More than 14,000 troops from 20 states are participating in FIREX '88, the largest artillery war games exercise in the United States since World War II.

The tour, he said, would give Koch "a firsthand look at guardsmen and reservists who are very deeply involved in training for their nation's defense" and show that their time is "at a premium."

"In addition, I would add that guardsmen from many states are already significantly involved in the war on drugs, in interdiction and support of law enforcement," Matthews said.

Utah National Guard officials said guardsmen and reservists now "share information with U.S. Customs officials" on suspected drug flights and ships coming into the United States and on desert landing sites for drug planes.