Carter and three other former state leaders -- known as The Elders -- were due to leave Pyongyang on Thursday after a "private" visit aimed at defusing tensions on the peninsula, as well as discussing the impoverished North's pleas for food aid.
The North has said it wants to rejoin international aid-for-disarmament talks, which it walked out of over two years ago in anger over a new round of U.N. sanctions for its second nuclear test and a long-range missile test.
"We are hearing consistently throughout our busy schedule here in Pyongyang that the North wants to improve relations with America and is prepared to talk without preconditions to both the U.S. and South Korea on any subject," Carter wrote in a blog on Wednesday on the Elders website (www.theelders.org)
|A South Korean looks at a TV screen showing footage of the public demolition of North Korea's cooling tower at its Yongbyon nuclear complex in 2008|
"The sticking point -- and it's a big one -- is that they won't give up their nuclear programme without some kind of security guarantee from the U.S."
The North has repeatedly stated it wants an assurance the United States will not attack it, as well as a peace treaty.
Some 30,000 American troops are based in South Korea, which is technically at war with its neighbor, having only signed a truce to end the 1950-53 Korean War .
"It is to my mind a tragedy that, more than 60 years after the Armistice that ended the Korean War, North and South Korea have not signed a peace treaty," Carter wrote.
"My country, the United States, is South Korea's guarantor, which creates enormous anxiety among the North Korean people and drains their political energy and resources."
ELDER STATESMEN MAY STILL MEET KIM JONG-IL
Carter and his team -- comprising former Irish President Mary Robinson, former Finnish President Martti Ahtisaari and ex-Norwegian Prime Minister Gro Brundtland -- have met the North's ceremonial head of state and foreign minister.
Experts say there is a possibility they will also meet North Korean leader Kim Jong-il and his son and heir apparent Kim Jong-un before departing for Seoul on Thursday.
Carter's visit comes as momentum builds toward a resumption of aid-for-disarmament talks involving the two Koreas, the United States, China, Japan and Russia.
South Korea, with Washington's backing, has demanded the North "show a responsible attitude" for last year's two deadly attacks on the peninsula for the talks to restart.
The North denies responsibility for the torpedoing of a South Korean warship last year, and said it shelled Yongpyeong island after South Korea test-fired artillery into its waters.
Shuttle diplomacy between the six-party envoys has increased in recent weeks, and China's nuclear envoy and his South Korean counterpart agreed in Seoul this week on a stage-by-stage process for restarting the talks.
However, both Seoul and Washington are skeptical about the North's sincerity about denuclearizing, citing its revelations last year of major advances in a uranium enrichment programme which could open a second route to make an atomic bomb.
Experts say the North already has enough fissile material from its plutonium programme to make about eight nuclear bombs.
Few people believe the secretive North will ever give up its pursuit of nuclear weapons, saying they serve as a deterrent against attack as well as being the ultimate bargaining chip.