PYONGYANG, North Korea (CNN) -- North Korean leader Kim Jong Il has been suffering from serious health problems, and may have had a stroke, a U.S. intelligence official told CNN Tuesday -- the same day Kim missed a parade celebrating the 60th anniversary of the Communist nation.

National Security Council spokesman Gordon Johndroe said the White House is aware of the reports, but has no additional information.

Kim's absence from the parade and events the night before revived questions about the president's health. The leader has denied reports that he suffers from heart disease and diabetes.

The second-in-command in North Korea, Kim Yong Nam, said there is no problem with Kim, the Kyodo News agency of Japan reported Wednesday. Naoko Aoki of the news agency said the second-in-command filled in for Kim at the parade.

A senior North Korean diplomat dismissed reports that Kim was ill as "a conspiracy plot," Kyodo reported.

"We see such reports as not only worthless, but rather as a conspiracy plot," Song Il Ho, North Korea's ambassador for normalization talks with Japan, was quoted as saying.

South Korean President Lee Myung-bak held a meeting Wednesday with his senior secretaries on the matter, a source at his office told the nation's Yonhap news agency.

"Lee discussed countermeasures to a possible serious illness of the North Korean leader during his unscheduled meeting with senior presidential secretaries," Yonhap quoted Cheong Wa Dae, a source at the presidential office, as saying. Watch the massive military parade in Pyongyang »

North Koreans filled Pyongyang's main square, which can hold about 100,000 people, she said.

Participating in the parade were paramilitary troops, which are not part of North Korea's regular army -- there were no members of the regular army, navy or air force, Aoki said. There were anti-aircraft and anti-tank artillery on display, but no tanks or missiles, she added.

Kim also holds the post of supreme commander of the Korean People's Army.

CNN's Brianna Keilar contributed to this report.

All About South Korea • North Korea • Kim Il-sung