ATMORE, Ala., Friday, June 6— A Ku Klux Klansman whose killing of a black teen-ager ultimately bankrupted the KKK faction that incited the crime was executed early today in Alabama's first execution for a white-on-black crime since 1913.

The inmate, Henry Francis Hays, 42, was convicted in the 1981 slaying of Michael Donald, a 19-year-old black man who was abducted at random from a Mobile street by two men, then beaten, cut and strangled. His body was strung up in a tree.

Gov. Fob James Jr. refused to grant clemency to Mr. Hays.

Prosecutors said the slaying was ordered by Klan leaders ''to show Klan strength in Alabama.'' Instead, the slaying wound up financially destroying the United Klans of America in 1987. A jury found the Klan liable in a wrongful-death case brought by Mr. Donald's mother and was ordered to pay $7 million.

The Klan had nowhere near that amount in assets. It had to sign over its Tuscaloosa, Ala., building to Beulah Mae Donald, who sold it for about $52,000 and bought a house. She has since died.

The last time a white person in Alabama was executed for killing a black person was 84 years ago.

Assistant Attorney General Joe Marston 3d said there was no bias involved in the record, just simple math. ''Most murders are black-on-black,'' he said. ''You'd have to do some very deep and difficult research on how many white-on-black crimes you have, and how many fall into capital murder categories.''

On Wednesday, in Huntsville, Tex., a man who shot a convenience store clerk and a gang leader who ordered the killing of a teen-age girl who had been raped, were executed as Texas tied its 1935 record for executions in a single year.

Dorsey Johnson-Bey, 30, who was convicted of killing a grocery store clerk, on March 23, 1986, became the 19th convicted killer to be executed by injection in the state this year. A little more than an hour later, Davis Losada, 32, convicted with three others in the killing of a 15-year-old girl, became the 20th.