On Wednesday, South Korea's National Intelligence Service reported to a parliamentary committee that it obtained intelligence reports showing Kim recently had surgery for an unspecified circulatory problem, and his condition had much improved, an agency official said.
The official, who spoke on condition of anonymity citing office policy, did not elaborate.
South Korea's Yonhap news agency, citing lawmakers briefed by the spy agency, reported that the 66-year-old Kim suffered a cerebral hemorrhage, but he remains conscious and "is able to control the situation."
The NIS also reported to lawmakers that Kim is in a "recoverable and manageable condition," and that the North is not in a "power vacuum," Yonhap said.
NIS officials said they could not confirm the Yonhap report.
Earlier in the day, North Korean officials denied that Kim may be ill or that there was anything unusual about his absence from the parade.
"There are no problems," Kim Yong Nam, Pyongyang's No. 2 leader and ceremonial head of state, told Japan's Kyodo News agency, referring to Kim Jong Il's absence.
Song Il Ho, a senior diplomat, said reports of Kim's illness are "worthless" and a "conspiracy plot," adding Western media "have reported falsehoods before," according to Kyodo's dispatch from Pyongyang.
It was not the first time North Korea had sent a message to the outside world through Kyodo. Kim Yong Nam also gave the news organization an interview two days after North Korea carried out its first-ever nuclear test blast in 2006.
In another indication that the North's leader is alive, Pyongyang's official Korean Central News Agency said Kim sent a birthday greeting Wednesday to Syria's leader.
Kim wished Syrian President Bashar Assad good health and success in efforts to make the country secure and prosperous, according to the Korean-language message carried by KCNA.
Early Wednesday, South Korean President Lee Myung-bak convened an emergency meeting in Seoul to discuss the situation with senior aides, an official at the presidential Blue House said.
Lee's office said in a statement after the meeting that the government will continue to follow the situation closely. It said Seoul had predicted the North's leader may not attend Tuesday's event, but did not elaborate.
Seoul's Defense Ministry said there has been no unusual movement in North Korea's military and the heavily armed border between the two sides remained calm.
North Korea's official Korean Central News Agency devoted its coverage Wednesday to stories celebrating the country's founding anniversary and gave no hint of Kim's condition. It is considered an absolute taboo for state media to discuss the North Korean leader's health in the totalitarian nation where he is revered almost as a demigod.
Speculation over Kim's condition spiked Tuesday after he did not appear at a parade commemorating North Korea's founding 60 years ago, one of the country's most celebrated holidays along with the birthdays of Kim and his late father, Kim Il Sung, the country's founding leader.
Kim, who has been rumored to be in varying degrees of ill health for years, took over the reclusive state upon the death of his father 14 years ago in a hereditary transfer of power. The younger Kim attended the parade on the 50th and 55th anniversaries and was widely expected to do so this year as well.
Since late 2002, North Korea has been locked in a standoff with the United States over its nuclear ambitions.
The country carried out its first nuclear test in 2006, but agreed last year to disable its nuclear facilities in exchange for economic aid and political concessions.
The negotiations, however, hit a snag again recently with the two sides at odds over how to verify North Korea's accounting of its nuclear programs. Washington has delayed its promised removal of Pyongyang from the U.S. terrorism blacklist.
Associated Press writers Eric Talmadge in Tokyo and Hyung-jin Kim in Seoul contributed to this report.