The younger Kim has been commander-in-chief of North Korea's huge military forces since 1994, but has yet to take on the highest state titles of president and general secretary of the Korean Workers' Party.
Information about the inner workings of the communist leadership is virtually non-existent, but speculation has focused on two possibilities: either protocol makes it inappropriate for a new leader to be inaugurated during the mourning period, or Mr Kim does not command the confidence of his party.
Food shortages, economic decline and continuing tensions with Pyongyang's deadly rivals in South Korea have encouraged rumours that Kim Jong Il's authority is under threat.
Yesterday, at ceremonies to mark the third anniversary of his father's death, senior members of the Worker's Party referred to him by military rather than state titles, but reaffirmed his status as Kim Il Sung's heir. "Long ago he most brilliantly solved the question of inheritance of the leadership in Korea, with a high sense of responsibility for Socialism and the future of the people," said the foreign minister, Kim Yong Nam, in a speech carried by the Korean Central News Agency. "Party members, officers and men of the People's Army, and all the people will forever believe in Comrade Kim Jong Il, and follow none but him."
Last month, North Korea's ambassador to Moscow said Mr Kim would take on the presidency soon after yesterday's ceremonies, but a report by the South Korean government this week predicted that this would not happen until October.
State television yesterday showed an unsmiling Mr Kim listening to speeches praising him in front of the presidential palace. Thousands of mourners were shown laying wreaths at a huge statue of the late "Great Leader".Reuse content