The leader, who missed Tuesday's celebration of his country's 60th anniversary, has periodically been reported ill. But the speculation this time assumes greater urgency.
Destruction of its nuclear cooling tower was important but largely symbolic.
The North's actions set the stage for another round in six-party talks, scheduled to take place next week in Beijing.
A US diplomat returns from talks in Pyongyang Monday with 18,000 pages supplied by North Korea on its nuclear facilities.
Pyongyang says it will release thousands of documents, long sought US officials, relating to its Yongbyon nuclear facility.