The uncertainty threatens to plunge one of Africa's largest and most populous countries - which is divided by a rebellion - into further chaos.
Confusion still surrounds the fate of Laurent Kabila, who is widely reported to have died following a shooting incident on Tuesday.
The uncertainty threatens to plunge one of Africa's largest and most populous countries - which is divided by a rebellion - into further chaos.
The Congolese Government still insists that the older Kabila is still alive, and that his son's appointment is only an interim measure.
The television showed pictures of his son, Joseph, in an attempt to quash rumours that he too had died in the shooting.
"Contrary to all the information broadcast by neighbouring countries' radio stations, the head of state, Mzee [old man] Laurent-Desire Kabila, is not dead," the TV said.
The report included pictures which were said to be of Joseph Kabila - the head of the Congolese army - shaking hands government with military officials after an extraordinary government meeting earlier on Wednesday.
Joseph Kabila, the report said, had been made acting head of the government and armed forces.
Reports of death
Foreign diplomats - led by former colonial power Belgium - began reporting the death of Laurent Kabila on Tuesday night.
Mr Kabila is believed to have been shot and seriously injured by his own bodyguards in the presidential residence in Kinshasa
On Wednesday, the Zimbabwean Government - Laurent Kabila's main ally in the war against rebels - announced that Mr Kabila had died while being flown to Zimbabwe for medical treatment.
The United States and the United Kingdom, as well as the head of the DR Congo peace negotiations, Botswana's Ketumile Masire, all say they believe Laurent Kabila to be dead.
But French Foreign Minister Hubert Vedrine, in Yaounde for the 21st Franco-African summit, said the Congolese president's death could not be confirmed.
Evacuation
In Kinshasa, security has been increased, and people are milling about on the streets wondering what is going on.
But Information Minister Dominique Sakombi said DR Congo's airports, closed in the wake of Tuesday's shooting, were being re-opened, and a curfew was being eased.
The shooting comes at a time of mounting discontent in the army, which has recently suffered setbacks in the civil war.
Three generals were arrested last week.
In Belgium, Prime Minister Guy Verhofstadt announced that the government was sending two military teams to neighbouring Gabon to prepare for a possible evacuation of foreign nationals.
About 2,500 Belgian citizens are currently resident in DR Congo, most of them concentrated in Kinshasa.
The BBC's West Africa correspondent, Mark Doyle, says the rebels may decide to take advantage of any confusion and try marching on the capital.
But he said it was also possible that the departure of Mr Kabila from the political scene would serve as a catalyst to peace talks being encouraged by the United Nations.
Kinshasa and its enemies have failed to abide by a series of ceasefire agreements, deepening the country's profound poverty.