Tens of thousands of mourners stood in the snow as the procession passed by. Soldiers stood with their heads bowed.
Kim died of a heart attack on December 17.
His youngest son and successor has rapidly gained prominence following his father’s death. Dressed in a dark overcoat, the younger Kim bowed his head slightly against the snow, and raised his right arm in salute.
Walking behind was Jang Song Thaek, Kim Jong Il’s brother-in-law and a vice-chairman of the powerful National Defence Commission, who is expected to play a crucial role in helping Kim Jong Un take power.
Kim Jong Il, who led the nation with an iron fist following his father Kim Il Sung’s death in 1994, died aged 69, according to state media.
Kim Jong Un is already being hailed as the “supreme leader” of the party, state and army.
A private ceremony is believed to have been held earlier today in the inner sanctum of the Kumsusan Memorial Palace with Kim Jong Un and top military and party officials.
Foreign dignitaries in the city had been asked to gather at a sports stadium shortly before noon to be taken to Kumsusan to see the hearse pass at the start of the funeral procession.
The young Kim made his public debut just last year with a promotion to four-star general and an appointment as vice-chairman of the Central Military Commission of the ruling Workers’ Party.
But in the days since his father’s death, the campaign to install him as the next leader has been swift, with state media bestowing him with new titles, including “great successor”, “supreme leader” and “sagacious leader”.
Footage showed images of swirling snow, the log cabin in Mount Paektu where Kim is said to have been born, and the mountain named after Kim Jong Il, where his name is carved into the rocky face in red.
Earlier, state television also replayed images of missiles being fired and the April 2009 long-range rocket launch that earned North Korea strengthened UN sanctions.
The US, South Korea and other nations called it a test for a missile designed to strike the United States. North Korea said the rocket sent a communications satellite into space.
Even as they mourned his father with dramatic displays of grief at memorials and at Kumsusan, North Korea’s officials have pledged loyalty to his son.
In an essay paying homage to Kim Jong Il, Workers’ Party spokesman Rodong Sinmun said: “Supreme leader of our party and people Kim Jong Un takes warm care of the people left by Kim Jong Il.”