South Korean and U.S. intelligence officials said the communist state's leader may have collapsed or suffered a stroke. Kim notably failed to appear at a military parade in Pyongyang marking the country's 60th anniversary on Tuesday.
In a rare interview with a foreign media outlet, the North's number two leader told Japan's Kyodo agency that there are "no problems" with Kim Jong-il's health.
"We see such reports as not only worthless, but rather as a conspiracy plot," Kim Yong-nam told the agency.
Seoul's Yonhap news agency said on Wednesday that the South Korean government is considering measures to be taken if Kim Jong-il's health deteriorates.
The agency quoted a high-ranking intelligence officer in the presidential office as saying "unusual goings-on" have been noticed in North Korea, indicating that Kim may have collapsed.
"It is certain that Kim Jong-il is sick. Taking various recent circumstances into consideration, Kim may have collapsed from an illness," the officer told the agency.
However, "it is also certain that he has not died. The Seoul government will soon disclose its position on the matter," he said.
Kim Jong-il has ruled North Korea since 1994, when he succeeded his late father Kim Il-sung, the communist state's founder. According to Soviet records, he was born in the Russian village of Vyatskoye near Khabarovsk, where his father commanded a military brigade in which Chinese and Korean exiles served.