Facing a potentially volatile situation in a country home to approximately 28,000 U.S. troops, President Obama and officials from administration are urging South Korea's leaders to remain calm following the announcement of the death of North Korean dictator Kim Jong-Il.

South Korean leaders are understandably nervous, administration officials told ABC News, given the recent history of North Korea's belligerent actions and the uncertain leadership position into which the new North Korean leader, Kim Jung-Un, steps.

While Kim Jon-Il had 14 years to endear himself to the public and solidify his power, Kim Jung-Un has had just three years, since his father's stroke in 2008. Because of his youth - he is in his late 20s - and relative inexperience, the youngest of Kim Jong-Il's three sons may feel he has to prove his "cojones," as one administration official put it.

"There's concern that Kim Jong-Un may now try to prove himself," said a senior government official, speaking on condition of anonymity due to the sensitive nature of the topic. "He's young, inexperienced, brash and untested. And while he had the support of his father, it's unclear if he has the respect of his generals."

This analysis is based on recent history. In 2010, as Kim Jong-Il was helping to solidify his son's role in the North Korean military, the country twice attacked South Korea in two of the most aggressive actions since the 1953 armistice that halted the Korean War.

In March 2010, North Korea torpedoed a South Korean warship, killing 46 sailors. In November 2010, North Korea shelled South Korea's Yeongyeong island, killing four South Koreans. It was in the midst of those acts of aggression when, in September 2010, Kim Jong-Un was appointed a four-star general in the People's Army. Three months after the shelling of Yeongyeong, Kim Jung-Un was appointed vice chairman of the National Defense Commission. Analysts speculate that Kim Jong-Un may have been asserting himself as an aggressive leader to chest-thump and win converts within the military apparatus.

What happens next on the Korean peninsula is not a far-off international dispute in which the U.S. can choose to involve itself or not. South Korea is home to roughly 28,000 US troops, and the U.S. is committed to South Korea's defense. One government official described the South Korean military as "subordinate" to the U.S. on the peninsula, though other officials disputed that characterization.

North Korea has tested two nuclear devices, one in 2006 and the other in 2009. In 2011, the county acknowledged that it had a uranium-enrichment program in addition to its well-known plutonium-enrichment program. American government officials speculate that North Korea has between 6 and 12 nuclear weapons, or at least enough material to build up to a dozen weapons, though there's no proof that North Korea has the ability to put the bombs on a delivery system that could reach the U.S. North Korea tested a Taepodong-2 inter-continental ballistic missile in 2009, but it failed after launch.

Senior White House officials say the concern about the North Korean military making a provocative action is less about the next few weeks - a state funeral is scheduled for December 28 - but the next few months, when Kim Jung-Un has to solidify his power base. Officials say more immediate concerns about Kim Jong-Un's action revolve around his country's missile and artillery programs, not the nuclear program.

Last night at around 10:30 pm ET, White House chief of staff Bill Daley informed President Obama that North Korea's State TV had announced the death of Kim Jong-Il. At midnight, President Obama spoke with South Korean President Lee Myung-bak. A White House statement read that: "The President reaffirmed the United States' strong commitment to the stability of the Korean Peninsula and the security of our close ally, the Republic of Korea. The two leaders agreed to stay in close touch as the situation develops and agreed they would direct their national security teams to continue close coordination."

National Security Adviser Tom Donilon spoke with his South Korean counterpart Chun Yung-woo.

The other wild card in this dynamic is President Lee who has suffered blows to his clout within country for a policy towards North Korea that some feel has given the North the upper hand. White House officials noted that President Obama has conducted significant outreach to President Lee, including a November 2009 visit to South Korea and an October 2011 state visit by President Lee to the White House, and asserted that the relationship between the two leaders is quite strong.

-Jake Tapper