North Korea's state news agency KCNA has called the dead leader's son Jong-un a "great successor" in what appears to be the first such mention of the late leader's youngest known son, who had been groomed to take over power.
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Earlier, North Korea urged its 24 million people to rally behind the 20-something heir as the nation mourned his father's death.
North Koreans mourn leader's death
South Korea, meanwhile, put its military on high alert, while people in the streets of Pyongyang broke into tears as they learned the news that Kim had died at the age 69 of heart failure. The United States said it was in close contact with allies South Korea and Japan.
Kim Jong Il. 'Great mental and physical strain' (Photo: AFP)
Kim is believed to have suffered a stroke in 2008, but he had appeared relatively vigorous in photos and video from recent trips to China and Russia and in numerous trips around the country carefully documented by state media. The communist country's "Dear Leader" - reputed to have had a taste for cigars, cognac and gourmet cuisine - was believed to have had diabetes and heart disease.
"It is the biggest loss for the party ... and it is our people and nation's biggest sadness," an anchorwoman clad in black Korean traditional dress said in a voice choked with tears. She said the nation must "change our sadness to strength and overcome our difficulties."
South Korean media, including Yonhap news agency, said South Korea put its military on "high alert" and President Lee Myung-bak convened a national security council meeting after the news of Kim's death. Officials couldn't immediately confirm the reports.
The news came as North Korea prepared for a hereditary succession. Kim Jong Il inherited power after his father, revered North Korean founder Kim Il Sung, died in 1994.
With son and heir-apparent Kim Jong Un (Photo: Reuters)
In September 2010, Kim Jong Il unveiled his third son, the twenty-something Kim Jong Un, as his successor, putting him in high-ranking posts.
US President Barack Obama has been notified of reports that the North Korean leader is dead and the US government is monitoring those reports, the White House said on Sunday.
US officials have been in close touch with allies in South Korea and Japan, the White House said.
"We remain committed to stability on the Korean peninsula, and to the freedom and security of our allies," White House press secretary Jay Carney said in a written statement.
AP and Reuters contributed to this report
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