Kim Jong-un has been groomed to succeed his father as the country's next leader since last year, when he was named a four-star general and vice chairman of the Central Military Commission of the ruling Workers' Party.
South Korea's intelligence chief Won Se-hoon still called for a close watch of developments in North Korea, telling lawmakers it is "unpredictable" whether Kim Jong-un can lead the country of 24 million people.
Defense Minister Kim Kwan-jin also weighed in on the issue, saying, "it is a matter that cannot be rashly predicted."
He also said South Korea and the United States are fully prepared for possible contingencies in North Korea, including its nuclear weapons programs. He did not give further details.
The caution comes as the North's state media stepped up efforts to idolize Kim Jong-un for a smooth transition of power.
North Korean state media began to describe Kim Jong-un as being "respected" as well as calling him a great successor and an outstanding leader who is identical to the late leader.
"All the party members, servicepersons and people should remain loyal to the guidance of respected Kim Jong-un," the North said Monday in a notice carried by the North's official Korean Central News Agency.
The new title of being respected is seen as the opening of a new era of Kim Jong-un, an inexperienced 20-something. Kim Jong-il was referred to as "Dear Leader" as he assumed power from his father, the country's founder Kim Il-sung, who died in 1994.
China and Russia, the two major allies of the North, appear to have endorsed Kim Jong-un as North Korea's new leader in condolence messages to the North.
Russian President Dmitry Medvedev addressed Kim Jong-un as "your respected excellency Kim Jong-un" in the message.
Chinese leaders also said they were convinced the Korean people will overcome their sorrow and display strength "under the leadership of Kim Jong-un."
Andrei Lankov, a North Korea expert at Kookmin University in Seoul, said he believed Kim Jong-un will be able to take over the country.
"The decision makers understand perfectly well that they should keep at least an outward appearance of unity, otherwise the situation might get out of control, leading to regime collapse," Lankov said.
In Pyongyang, Kim Jong-un mourned the death of his father at a solemn ceremony. Kim Jong-un and other top officials "visited the bier of Kim Jong-il to express deep condolences with the bitterest grief," the KCNA said in a separate dispatch.