South Korean President Moon Jae-in and North Korean leader Kim Jong Un at the Paekhwawon State Guesthouse in Pyongyang (Picture: Pyeongyang Press Corps).

The leader of North Korea has agreed to dismantle his main nuclear complex but only if the United States does the same.

Kim Jong Un agreed on the second day of meetings with his South Korean counterpart President Moon Jae-in on an ambitious programme meant to tackle soaring tensions between the two countries last year.

Mr Kim promised to accept international inspectors to monitor the closing of a key missile test site and launch pad and to visit Seoul soon, and both leaders vowed to work together to try to host the Summer Olympics in 2032.

But their joint statement appeared to fall short of the major steps many in Washington have been looking for.

Such steps include a commitment by Mr Kim to provide a list of North Korea's nuclear facilities, a timeline for closing them down, or an agreement to allow international inspectors to assess progress or discover violations.

US President Donald Trump, described the Korean leaders' agreements as "Very exciting!" in a tweet.