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His removal leaves no clear No. 2 under Mr. Kim, whose inner circle now includes Vice Marshal Choe Ryong-hae, Premier Pak Pong-yu and the ceremonial head of state, Kim Yong-nam.

In an interview aired Sunday on ABC’s “This Week,” U.S. Secretary of State John F. Kerry said Jang’s execution is “an ominous sign of the instability” of North Korea and underscores the urgency of denuclearizing the Korean Peninsula.

“To have a nuclear weapon, potentially, in the hands of somebody like Kim Jong-un just becomes even more unacceptable,” Mr. Kerry said.

What will happen next in Pyongyang remains unclear, but North Korea watchers will be closely following the second anniversary of the death of Mr. Kim’s father, Kim Jong-il, on Tuesday for clues. Of particular interest is whether Jang’s wife, Kim Kyong-hui, the younger sister of Kim Jong-il, will be present in official ceremonies.

Her name appeared in a state media dispatch late Saturday alongside top officials on a funeral committee for fellow senior Workers’ Party official Kim Kuk-thae, who died Friday.

Mrs. Kim, 67, has risen through the ranks in recent years and holds a slew of top posts. Analysts said the dispatch suggested that her political standing hasn’t been immediately affected by her husband’s execution and that she may have even given her nephew the green light to fire Jang — but not to have him executed.

“She may have opposed Jang’s death sentence, but she could have agreed on Jang being dismissed,” said analyst Hong Hyun-ik from the private Sejong Institute in South Korea.

Mrs. Kim and Jang, who married in 1972, had a dysfunctional marriage in recent years, and their only daughter committed suicide in 2006 while studying in Paris, according to South Korean media reports.

Mr. Hong said that if her health condition allows it, Mrs. Kim is expected to join other top officials at Tuesday’s ceremonies marking the second anniversary of Kim Jong-il’s death.

Mrs. Kim’s public activities have been sharply reduced in recent months amid media reports that she suffers liver, heart and other ailments.

• Associated Press writer Hyung-jin Kim in Seoul contributed to this report.