An unnamed US intelligence official told reporters: "It does appear that Kim Jong-Il has had a health setback, possibly a stroke."
The official said Kim appeared to have become ill in "the last couple of weeks".
The US state department later said it could not confirm the reports.
The BBC's John Sudworth, in the South Korean capital Seoul, says rumours were already rife about his well-being before the rally.
But Mr Kim's absence from the parade - he was not seen in any of the TV coverage of the event - will prompt further speculation, especially given the symbolic importance of the anniversary.
This is especially the case, our correspondent says, given that Mr Kim oversaw similarly triumphant occasions for North Korea's 50th and 55th anniversaries.
The anniversary comes amid an impasse in international efforts to urge North Korea to abandon its nuclear programme.
On Monday, state-run television channel KRT showed footage of the North's cabinet holding a large indoor gathering to mark the anniversary.
North Korean leader Kim Jong-il is notoriously reclusive
The cabinet released a statement, picked up by monitors in Seoul, saying that North Korea had a powerful army that would "mercilessly punish invaders".
According to South Korean media, the main parade on Tuesday was to be the largest ever staged by its northern neighbour.
"The North probably wants to boost the image of its military might in order to cement unity within the country and secure a better position in the denuclearisation negotiations," a South Korean government source told JoongAng Ilbo newspaper.
The future direction of North Korea is tightly linked to the personality of the country's reclusive leader.
Mr Kim has not been seen in public since early last month, giving rise to speculation he could be seriously unwell.
Mr Kim has been known to disappear from public view for extended periods before, and has always returned eventually, but this time the rumours of ill health have been given added impetus by news that a team of Chinese doctors was recently summoned to examine him.
The celebrations are taking place amid rising tensions between Pyongyang and the international community.
North Korea agreed in February 2007 to give up its nuclear ambitions in return for aid and diplomatic concessions, but the progress of the deal has been far from smooth.
After a long delay, Pyongyang handed over details of its nuclear facilities in June 2008.
In return, it expected the US to remove it from the list of state sponsors of terrorism, which the US has yet to do, so the North now appears to be starting to reassemble its main nuclear plant.
Meanwhile the World Food Programme estimates that North Korea is suffering from a serious food shortage.
The North has relied on foreign assistance to help feed its 23 million people since its state-controlled economy collapsed in the mid-1990s.
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