Kyodo gave no further details although it also quoted Song Il-ho, a senior North Korean diplomat, as saying that any reports Kim was unwell were "not true" and "worthless".
Song, who oversees North Korea's relations with Japan, said such speculation was seen as a "conspiracy plot".
"I believe the aim is to form a public opinion on something that is not true," Kyodo reported him as saying. "Western media have reported falsehood before."
|Kim has long been rumoured to suffer from diabetes and heart problems [AFP]
An earlier report by South Korea's Yonhap news agency quoted an unnamed South Korean official as saying that Kim appeared to have "collapsed" and was ill, but still alive.
On Wednesday, South Korea's president, Lee Myung-bak, convened an emergency meeting in Seoul with senior aides to discuss the situation.
Tuesday's anniversary celebrations in North Korea had been closely scrutinised for any appearance by the country's reclusive leader following weeks of speculation over his health.
The celebrations included a massive military parade through the centre of Pyongyang – an event usually overseen by Kim, known to North Koreans as the "Dear Leader".
Leonid Petrov, a North Korea expert at the Australian National University in Canberra, told Al Jazeera he believed poor health was the most likely explanation
"His health has not been well in recent months," Petrov said, noting that Kim had seemed increasingly unwell during his most recent recorded public appearances.
The question now, he said, was who could take over, whether it might be one of Kim's three sons or a member of the country's powerful armed forces.
Recent rumours, attributed to South Korean diplomats in Beijing, had suggested that Kim may have fallen ill several weeks ago, with a group of Chinese doctors dispatched to Pyongyang to treat him.
The North Korean leader is thought to have suffered for years from diabetes and heart problems.
On Tuesday a US intelligence official said reports indicated that Kim had "suffered a health setback, potentially a stroke".
She said there have been no signs of a change in governing power and that assessing whether Kim was still capable of governing would "call for a lot of speculation".