PYONGYANG, May 27 (Xinhua) -- Kim Jong Un, top leader of the Democratic People's Republic of Korea (DPRK), has expressed his "fixed will" to hold a summit with U.S. President Donald Trump, when he met with South Korean President Moon Jae-in Saturday at the truce village Panmunjom, said Korean Central News Agency (KCNA) Sunday.

Kim also promised to further push forward the peace process on the Korean Peninsula by working for the goal of denuclearization and improving inter-Korean ties.

During the meeting, Kim thanked Moon for the efforts made by him for the DPRK-U.S. summit scheduled for June 12, and expressed his fixed will on the historic DPRK-U.S. summit talk, said KCNA.

"Kim Jong Un told Moon Jae-in to positively cooperate with each other as ever to improve the DPRK-U.S. relations and establish mechanism for permanent and durable peace," said the report.

The surprise inter-Korean summit came soon after Trump said he remained open to a summit with Kim in Singapore on June 12.

Kim and Moon met for the second time within one month on Saturday on the northern side of the demarcation line of Panmunjom.