TEGUCIGALPA, Honduras (AP) _ A soldier in the Honduran air force has been arrested in the shooting death of an American soldier at an air base in this Central American country, military intelligence sources said Thursday.

The soldier was arrested Saturday night, the day Staff Sgt. Randall J. Harris was killed at Palmerola air base, and is in custody of the Honduran air force, the sources said.

The suspect ''has been subjected to a series of interrogations, including the lie detector test, in which he has contradicted himself repeatedly,'' one of the sources said, speaking on condition of anonymity.

He declined to release the man's name ''because the investigation is continuing.'' It was not clear whether the man had been charged.

The Honduran soldier, who was in uniform at the time, had left his guard post outside the base, 36 miles northwest of Tegucigalpa, when Harris was shot with an M-16 rifle, the source said.

''That weapon was found in the belongings of the arrested man and, in addition it is a rifle that is no longer used by our soldiers,'' he said.

''We have sent the bullets found in Harris' body to the United States, where there are sophisticated centers of ballistic investigation to determine the situation definitely,'' he said.

He said authorities have no motive for the killing.

''We don't know the causes of what happened, but the investigation continues,'' the source said.

Harris, 34, Of Wilmington, Ohio, was shot once in each leg and once in the back as he was supervising military police about 400 yards inside the main gate of Palmerola air base.

He was with the 978th Military Police Company from Fort Bliss, Texas, which is serving a four-month temporary tour at Palmerola, headquarters for U.S. operations in Honduras.

Honduran police have said privately that Harris was killed in an area of the base used only by U.S. troops. More than 150 Honduran soldiers were on duty outside the base, they said.

It was not clear why the arrest had not been disclosed earlier.

Lt. Col. James Lawson, a spokesman at Fort Bliss, said Tuesday a suspect had been arrested and said only that he was not a U.S. soldier.

However, Capt. Ron Eschmann, U.S. military press officer at Palmerola, denied the report.

U.S. troops have trained in Honduras since 1983 under a nearly continual program of joint maneuvers.

The largest exercise, involving more than 40,000 American military personnel, was a three-week operation that ended in mid-May.

In June 1986, an American soldier was killed and another seriously wounded by a Honduran soldier who was in their custody. Last December, a woman fist sergeant was killed when one of her Honduran companions began shooting into the air in a nightclub at the Caribbean coast resort of Tela, 100 miles north of Tegucigalpa.