Before the ceremony began, hundreds of thousands of mourners bowed their heads for a moment of silence.
They packed the capital's main square where the new supreme leader watched from a balcony.
The ceremonial head of state told the crowd that Kim Jong Un inherits his father's ideology, character and revolutionary cause.
The unequivocal public backing for Kim Jong Un at his father's memorial provides a strong signal that government and military officials have unified around him in the wake of Kim Jong Il's death. He died of a heart attack on Dec. 17 at the age of 69.
There are questions outside North Korea about wheather Kim Jong Un, who is in his late 20s, is ready to lead a nation engaged in long-stalled negotiations over its nuclear program and grappling with decades of economic hardship and chronic food shortages.
Kim Jong Il led 24 million people with absolute power for 17 years. He inherited power from his father, North Korea founder Kim Il Sung, who died of a heart attack in 1994, in what was the communist world's first hereditary succession.
The Associated Press contributed to this report.