South Korea joined a US-led program to block shipments of nuclear material. In Japan, a lawmaker urged first-strike capability.
Monday's explosion – the latest in a series of hard-line moves by Pyongyang – may have been 20 times more powerful than its last test in 2006.
The move comes as South Korea and the US begin a large-scale joint military exercise.
The Yongbyon reactor could be operational again within a year.
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.
The North's actions set the stage for another round in six-party talks, scheduled to take place next week in Beijing.
Pyongyang says it will release thousands of documents, long sought US officials, relating to its Yongbyon nuclear facility.