SEOUL, South Korea — The execution of the uncle of Kim Jong-un, North Korea’s leader, had its roots in a firefight between forces loyal to Mr. Kim and those supporting the man who was supposed to be his regent, according to accounts that are being pieced together by South Korean and American officials. The clash was over who would profit from North Korea’s most lucrative exports: coal, clams and crabs.

North Korean military forces were deployed to retake control of one of the sources of those exports, the rich crab and clam fishing grounds that Jang Song-thaek, the uncle of the country’s untested, 30-year-old leader, had seized from the military. In the battle for control of the fishing grounds, the emaciated, poorly trained North Korean forces “were beaten — very badly — by Uncle Jang’s loyalists,” according to one official.

The rout of his forces appears to have been the final straw for Mr. Kim, who saw his 67-year-old uncle as a threat to his authority over the military and, just as important, to his own family’s dwindling sources of revenue. Eventually, at Mr. Kim’s order, the North Korean military came back with a larger force and prevailed. Soon, Mr. Jang’s two top lieutenants were executed.

The two men died in front of a firing squad. But instead of rifles, the squad used antiaircraft machine guns, a form of execution that according to South Korean intelligence officials and news media was similar to the one used against some North Korean artists in August. Days later, Mr. Jang himself was publicly denounced, tried and executed, by more traditional means.