South Korea's President Moon Jae-in and U.S. President Donald Trump plan to hold a summit next month in Washington, D.C., Yonhap News Agency reported on Friday, citing the South Korean presidential office Cheong Wa Dae.

Moon will arrive in the U.S. on April 10 to hold a summit with Trump the following day, his office said. They will have in-depth talks to discuss ways to strengthen the Seoul-Washington alliance and to coordinate their stance on the Korean Peninsula issue "through complete denuclearization," Yoon Do-han, senior secretary for public relations, said as he briefed the media.

It will be their first meeting since last month's summit between Trump and the Democratic People's Republic of Korea (DPRK)'s leader Kim Jong Un in Hanoi.

The second summit between Trump and Kim ended without reaching an agreement.

Soon after the summit, Trump updated Moon on his meeting with Kim over the phone en route to Washington. Trump said his administration would "continue the conversations" with Kim and continue to coordinate closely with the allies.

Trump said there was a "gap" in what the DPRK and the U.S. were pursuing. Kim demanded relief from sanctions against Pyongyang "in their entirety" in exchange for denuclearizing a "large portion" of the DPRK's nuclear program, something the U.S. could not agree.

On the other side, DPRK Foreign Minister Ri Yong Ho said at a separate news conference in Hanoi that "what we proposed was not the removal of all sanctions, but they are partial removal," adding that the DPRK only asked those sanctions impeding the livelihood of its people to be removed first.

A Blue House spokesperson, however, noted that it seemed clear that the two leaders have made "more meaningful progress" than ever as they expanded the scope and depth of their understanding of each other's positions through the two-day summit in the Vietnamese capital.