North Korean leader Kim Jong-un has reportedly expressed his "fixed" will to hold talks with United States President Donald Trump during his latest summit with South Korean President Moon Jae-in.

The North's official Korean Central News Agency (KCNA) on Sunday reported that the two Korean leaders held their second summit on Saturday at the Tongilgak on the northern side of the truce village of Panmunjeom.

The report said that the North Korean leader thanked Moon for his efforts for the June 12 U.S.-North Korea summit, expressing his firm commitment to the historic summit with Trump. It is the first time the North Korean media said that the summit will be held on June 12.

The KCNA said that in the summit with Moon, Kim proposed that the two Koreas continue active cooperation for efforts to improve Washington-Pyongyang relations and establish a lasting peace on the Korean Peninsula. It added that the two leaders reached a "satisfactory" agreement on issues discussed at the summit.