SEOUL, South Korea — As he was confessing to crimes that would lead to his execution, the doomed uncle of North Korea’s leader suggested that he hoped the country’s many economic woes would drive the military to overthrow the Kim dynasty, the state-run news agency said.

The statement, if true, was shocking for a country that normally hides any hint of disloyalty, has not publicized a coup attempt in decades and has not released a detailed explanation of a purge to its people — much less to the world. But even if the uncle, Jang Song-thaek, did not utter such treason, the laundry list of alleged crimes the North Koreans published is notable for its admission of instability in the hermetic nation and suggests that at least some see flaws in its debilitated state-run economy.

“I was going to stage the coup by using army officers who had close ties with me or by mobilizing armed forces under the control of my confidants,” the North’s Korean Central News Agency on Friday quoted Mr. Jang as having said during his court-martial. “I thought the army might join in the coup if the living of the people and service personnel further deteriorate in the future.”

As analysts scrambled Friday to make sense of the execution — many had doubted that the leader, Kim Jong-un, would kill a relative — and the highly unusual way the news rolled out, they advanced myriad theories for why Mr. Kim killed the man who was supposed to be his mentor. The biggest divide was whether the purge suggested Mr. Kim had fully taken charge of his country two years after his father’s death or, instead, was severely weakened by the reported betrayal.