The body of Kim Jong-il is lying in state in the capital Pyongyang as organised public mourning continues in streets and halls.
State media hailed the new leader, 27, as “the outstanding leader of our party, army and people”.
The UK’s consul in Pyongyang, Barnaby Jones, said foreign diplomats had been greeted by Kim Jong-un, seeming to confirm that he is indeed now in charge.
Kim Jong-un led a solemn procession of mourners on Tuesday past the body of his father, displayed on a bier under glass in a hall of the mausoleum where the embalmed body of Kim Il-song is kept.
State media heaped praise on the “Great Successor”, describing him as a “lighthouse of hope” for a country awash in a “sea of tears and grief.”
At least some of the mass wailing and weeping on the streets of Pyongyang is an expression of genuine grief, our correspondent says.
Rafael Wober, a journalist with the Associated Press, one of the few foreign media organisations to be given access to Pyongyang, described the moment news of the death broke on Monday:
“Well, the announcement came as a complete surprise. I went out, I could see immediately in the corridors hotel staff crying, in the restaurant and the shop downstairs, hotel staff in tears, sobbing.”