She said the uncertainty may be contributing to a recent rise in hostile rhetoric coming from the reclusive communist state as well as the North's apparent moves to launch a long-range missile.
Her comments, made to reporters during a flight to South Korea from Indonesia, were a rare if not unprecedented public acknowledgment from a senior U.S. official that the secretive nation may be preparing for a leadership change following reports that Kim had a stroke last year.
Clinton said South Korea is particularly worried "about what's up in North Korea, what the succession could be, what it means for them, and they are looking for us to use our best efforts to try to get the agenda of denuclearization and nonproliferation back in gear."
"Everybody is trying to sort of read the tea leaves as to what is happening and what is likely to occur, and there is a lot of guessing going on," Clinton said, referring to talks between Chinese, South Korean, Japanese and U.S. officials about the situation in the North.
"But there is also an increasing amount of pressure because if there is a succession, even if it's a peaceful succession, that creates more uncertainty and it may also encourage behaviors that are even more provocative as a way to consolidate power within the society," she said.
Kim, 67, inherited leadership from his father, North Korea founder Kim Il Sung, in 1994, creating the world's first communist dynasty. He rules the nation of 23 million people with brutal authority, allowing no opposition or dissent.
His failure to show up last September for a military parade marking the country's 60th anniversary spurred questions about the health of a man believed to have diabetes, heart disease and other chronic ailments.
South Korean and U.S. officials later said Kim suffered a stroke and underwent brain surgery in August. North Korean officials have steadfastly denied Kim was ever ill.
However, state-run media made no mention of Kim's public appearances for weeks last fall, feeding fears that his sudden death without naming a successor could leave a power vacuum and spark an internal struggle.
Kim's father had cultivated a powerful cult of personality that encompassed him and his son and recent dispatches in North Korea's state-run Korean Central News Agency have stressed the importance of bloodline and inheritance in what is seen as references to the succession plan.
Kim Jong Il is believed to have at least three sons: Kim Jong Nam, in his late 30s; Kim Jong Chul, in his late 20s; and Kim Jong Un, a son in his mid-20s by another companion.
The eldest is believed to have been the favorite to succeed his father until he was caught trying to enter Japan on a fake passport in 2001, reportedly to visit Tokyo Disneyland.
Last month, South Korean news agency Yonhap said the youngest, Kim Jong Un, was named Kim's heir apparent.
And, on Thursday, citing unnamed sources in Beijing, Yonhap said Kim Jong Un had registered his candidacy for March 8 parliamentary elections in a sign the son is poised to become the country's next leader.
Fueling speculation of possible power struggle, the North's state-run news agency reported last week that Kim Jong Il had replaced his defense minister and chief of the military's general staff.
Clinton, who will visit China over the weekend, said she would be seeking advice in Seoul and Beijing about how to resume stalled six-nation disarmament talks given questions about Kim's health and who is now or may soon be in charge in Pyongyang.
"Our goal is to try to come up with a strategy that is effective in influencing the behavior of the North Koreans at a time when the whole leadership situation is somewhat unclear," she said.
"You add to the already difficult challenge of working with the North Koreans the uncertainties that come from questions about potential succession, this is a difficult undertaking," Clinton said.
Just hours before Clinton arrived in Seoul, the North Korean military issued a statement accusing South Korean president Lee Myung-bak of misusing "nonexistent nuclear and missile threats" as a pretext to invade.
"The Lee Myung-Bak group of traitors should never forget that the (North) Korean People's Army is fully ready for an all-out confrontation," said the statement.
Clinton is to meet with Lee on Friday and said she would speak to him and others about how to defuse tensions between the two Koreas. "We don't want it to spiral up," she said.
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