GLENWOOD SPRINGS, Colo. -- Authorities said Thursday that they have a suspect in the recent shooting death of Qwest Communications executive Jeff Garrett.

"We have recovered the weapon, we have a witness, and we have a suspect," said Lou Vallario, the Garfield County Sheriff.

Vallario told reporters Thursday afternoon that investigators believe a Mexican national -- who has since reportedly fled to Mexico -- is responsible for the May 14 fatal shooting.

The suspect's name was not released.

Garrett died after being shot in the upper right chest while turkey hunting with two friends.

The shooting happened in the East Elk Creek area, north of New Castle, Colo. Garrett died on Bureau of Land Management property around 8,000 feet in elevation. Both friends were cleared in the shooting.

Vallario says the shooting suspect worked at the Bear Wallow Ranch just outside New Castle, near the area where Garrett was shot. A woman who answered the phone at the ranch said she was not aware of the case and declined comment.

Investigators said a co-worker of the suspect witnessed the shooting, and told them that the suspect knew what he had done before leaving the country. The co-worker reportedly told investigators that he was with the suspect when they heard turkey calls coming from heavy brush near the ranch perimeter and that the suspect fired in the direction of the calls, thinking they came from a turkey.

Garrett was dressed in full camouflage. Turkey hunters aren't required to wear blaze orange because turkeys have sharp eyesight and must be called to within shotgun range.

While only shotguns are allowed in the spring turkey hunt, Garrett was shot with a .22-caliber rifle.

The shooting is being treated as a homicide.

Garrett was an Aurora resident and worked as Qwest's assistant vice president for Colorado and a state lobbyist for the company. He is survived by his wife, Charlotte, and children Olivia, 3, and Adam, 1.

Charlotte attended Thursday's news conference in Glenwood Springs and said her husband's death was "devastating."

"Jeff was a thoughtful husband, a proud father, a loving son, a protective brother and, to many people, a funny and caring friend," she said.

U.S. Congressman Tom Tancredo (R-Littleton) issued a statement in response to Thursday's news conference naming a Mexican national as the suspect in the shooting.

"It is shameful that illegal aliens can so easily cross our porous borders or overstay their visas with such impunity. It is tragic that an illegal alien can commit a murder in this country and evade American justice by slipping back across the border," his statement said in part.

Another Mexican national has been charged in the May 8 slaying of a Denver police officer and was arrested after fleeing to Mexico. Raul Gomez-Garcia is also accused of wounding a second police officer in the same shooting. The Denver District Attorney's Office is attempting to extradite Gomez-Garcia to face trial in Colorado.