Pyongyang is thought to be preparing for launch its longest-range Taepodong missile in what analysts say is an attempt to gain Washington's attention.
The rocket is believed to be theoretically capable of hitting targets as far away as the US west coast, although it has never flown successfully.
Speaking in Tokyo two days earlier as she began her first foreign trip since taking office, Clinton said that any North Korean missile launch would be "very unhelpful".
During her flight to South Korea on the third leg of her four-nation tour of Asia, Clinton voiced US concern over a potential change in Pyongyang's ruling structure.
Clinton said that South Korea was worried "about what's up in North Korea, what the succession could be, what it means for them".
"They are looking for us to use our best efforts to try to get the agenda of denuclearisation and nonproliferation back in gear," she said.
Six party talks between North and South Korea, China, Japan, Russia and the US aimed at restricting North Korea's atomic programmes in exchange for economic and diplomatic incentives began in August 2003 but stalled in December 2008.
Last month, the North announced it was scrapping all agreements with the South, including a 1991 pact that recognised the Northern Limit Line (NLL), a sea border drawn unilaterally by US-led United Nations forces after the 1950-1953 Korean war.
The US secretary of state has wrapped up a two-day visit in Indonesia, the world's largest Muslim nation, where she praised Jakarta's transformation from an autocracy to a "vibrant democracy".
After South Korea, Clinton will go to China, the last stop on an Asian tour that also includes Japan.