During a live broadcast delivered by President Moon Jae-in's chief press secretary Yoon Young-chan, he said Moon and North Korean leader Kim Jong-un also agreed to make public when North Korea dismantles the northern test site.
Kim said he would invite security experts and journalists to the North.
"Some say that we are terminating facilities that are not functioning, but you will see that we have two more tunnels that are bigger than the existing ones and that they are in good condition," Yoon quoted Kim as saying.
"Although I am inherently resistant toward America, people will see that I am not the kind of person who fires nukes at South Korea, the Pacific or America," he said. "Why would we keep nuclear weapons and live in a difficult condition if we often meet with Americans to build trust and they promise us to end the war and not to invade us?"
Kim said he will not repeat the "painful history of the Korean War," adding, "Concrete measures are necessary to stop any accidental military confrontation from happening."
He also agreed to unify the time zones used in South and North Korea, where Seoul is 30 minutes ahead of Pyongyang.
"I feel sad to see that there are two clocks hung on the wall of the Peace House, one for Seoul time and the other for Pyongyang time," he said. "Since it is us who changed the time standard, we will return to the original one. You can make it public."
Last month, the North said it would dismantle the Punggye-ri site. It conducted all six nuclear detonations at the Punggye-ri facility in North Hamgyong Province. The first test was carried out Oct. 9, 2006, followed by a second one on May 25, 2009. Additional tests were conducted on Feb. 12, 2013, Jan. 6 and Sept. 9 in 2016. The sixth and most recent one was carried out Sept. 3, 2017. (Yonhap)