SINGAPORE, June 12 (Xinhua) -- Kim Jong Un, top leader of the Democratic People's Republic of Korea (DPRK), agreed Tuesday with U.S. President Donald Trump to complete denuclearization of the Korean Peninsula in exchange for security guarantees.

Kim and Trump signed a joint statement after their meeting -- the first between a sitting U.S. president and a DPRK leader -- at the Capella Hotel in Singapore's resort island of Sentosa.

In the joint statement, Trump committed to providing security guarantees to the DPRK, while Kim reaffirmed his firm and unwavering commitment to complete denuclearization of the Korean Peninsula.

The two leaders conducted a "comprehensive, in-depth and sincere exchange of opinions" on issues related to the establishment of a new DPRK-U.S. relationship and building a lasting and robust peace regime on the peninsula, the joint statement said.

They agreed to commit to establishing new DPRK-U.S. relations "in accordance with the desire of the peoples of the two countries for peace and prosperity."

The statement said the two leaders are convinced that the establishment of new DPRK-U.S. relations will contribute to the peace and prosperity of the Korean Peninsula and the world, and recognize that mutual confidence building can promote the denuclearization of the peninsula.

Pyongyang and Washington will join their efforts to build a lasting and stable peace regime on the peninsula, according to the joint statement.

Reaffirming the Panmunjom Declaration, which South Korean President Moon Jae-in and Kim signed after the third inter-Korean summit on April 27 at the border village of Panmunjom, the DPRK agreed to commit to working toward complete denuclearization of the Korean Peninsula, it added.

Pyongyang and Washington also agreed to commit to recovering the remains of prisoners of war and those missing in action during the 1950-53 Korean War, including an immediate repatriation of those already identified.

Kim and Trump acknowledged that the summit was of great significance in helping the two countries overcome decades of tension and hostilities and open up a new future in their relations.

They pledged to implement their agreement fully and expeditiously, concurring to hold follow-on negotiations to be led by U.S. Secretary of State Mike Pompeo and a high-level DPRK official at the earliest possible date.

The two leaders, the document said, have committed to cooperating for the development of new DPRK-U.S. relations and for the promotion of peace, prosperity and security of the Korean Peninsula and the rest of the world.

Kim and Trump started their first summit with a historic handshake that lasted for several seconds in front of a row of the national flags of the two countries.

"This is just a new beginning," Trump said while shaking hands with Kim.

Kim, dressed in a dark suit, and Trump, sporting a red tie, talked in a corner of the hotel corridor for a few minutes before they walked along the passage into the meeting room and sat down in front of journalists.

"The way coming here was not easy," Kim said.

"We had the past that grabbed our ankles and old prejudices and practices that covered our eyes and ears. We are here after overcoming all these," he said.

Predicting a success of the summit, Trump said it was "an honor" to meet with Kim face-to-face and that he would have "a terrific relationship" with the DPRK leader.

They met one on one for about 40 minutes, with only translators at their sides, before having an expanded meeting attended also by their key security and diplomatic aides.

On the DPRK side, Kim Yong Chol and Ri Su Yong, two vice chairmen of the Workers' Party of Korea (WPK) Central Committee, and Foreign Minister Ri Yong Ho were present.

Accompanying Trump were White House Chief of Staff John Kelly, National Security Advisor John Bolton, and Secretary of State Mike Pompeo.

"Working together, we will get it taken care of," Trump said at the beginning of the expanded discussions, forecasting that he and Kim will solve "a big problem and a big dilemma."

Kim said he will "cooperate with President Trump to resolve the challenges ahead" and to overcome the skepticism and speculations about their summit.

More officials took part in the working lunch, with the additional participants on the U.S. side, including White House Press Secretary Sarah Sanders, National Security Council Senior Director for Asia Matt Pottinger, and senior diplomat Sung Kim, who has led substantive talks with Pyongyang into the summit.

Since taking over his country's leadership in late 2011, Kim had made only three known trips to foreign countries before the Singapore visit. He traveled to China twice and to the South Korean side of the truce village of Panmunjom.