"I believe North Korea-U.S. relations will improve as now is the time for all countries to reconcile," Kim told reporters Tuesday at the John F. Kennedy Airport, South Korea's Yonhap News agency reported.
During his visit, Kim, former North Korean chief nuclear negotiator at the six-nation talks on his country's denuclearization, planned to meet with Stephen Bosworth, U.S. special representative for North Korean policy, Kyodo News reported.
There were no other details about his trip or whether he would be meeting other U.S. officials.
The six-nation talks among China, the United States, the two Koreas, Japan and Russia broke down in 2008 after the North walked out to protest U.N. condemnation of its long-range missile tests. The North conducted a second nuclear test in May 2009.
Kim's trip comes after South and North Korean officials held informal talks last Friday on the sidelines of a regional forum on the Indonesian resort island of Bali. After that meeting, U.S. Secretary of State Hillary Clinton announced the North Korean visitor had been invited to New York, the Voice of American reported.
One analyst told VOA the Bali meeting appeared to be setting the stage for a restart of the nuclear disarmament talks.
Tensions have risen on the Korean Peninsula since the six-way talks stalled. South Korea blames the North for the sinking of its warship in the Yellow Sea last year. The North also shelled a South Korean island in November. The two incidents resulted in the deaths of 50 people.