U.S. President Donald Trump speaks during a meeting with South Korean President Moon Jae-In at the Lotte New York Palace hotel during the United Nations General Assembly in New York, Monday. AP

South Korean President Moon Jae-in and U.S. President Donald Trump on Monday discussed plans for a second meeting between Trump and North Korean leader Kim Jong-un, agreeing they would work on it together, the White House said.

Moon and Trump met in New York on the sidelines of the United Nations General Assembly following a third summit between the South Korean and North Korean leaders last week.

Moon shared the outcome of that meeting with Trump, including Kim's renewed commitment to the complete denuclearization of the Korean Peninsula, the White House said in a readout.

"President Trump commended President Moon on conducting a successful third inter-Korean summit with Chairman Kim, and noted that there remained much work to be done to accomplish their mutual goal of achieving the final, fully verified denuclearization of North Korea," the statement said.

It also said the two men agreed that sanctions on North Korea had to be maintained through "vigorous enforcement" to make sure the regime understands that denuclearization is the only way to economic prosperity and lasting peace on the peninsula.

Moon, Trump discuss 'corresponding measures' for NK denuclearization 2018-09-25 08:24  |  North Korea
"Both leaders also discussed plans for a second summit between President Trump and Chairman Kim in the not too distant future and committed to closely coordinate on next steps," the White House added.

In remarks to the press, Trump said the location and date of the second summit would be announced "within a pretty short period of time."

He met Kim in Singapore in June -- the first meeting between a U.S. and North Korean leader -- and came away with the North's commitment to the "complete denuclearization" of the Korean Peninsula in exchange for security guarantees from the U.S.

As progress on the deal stalled, Moon met with Kim last week to help revive the negotiations. (Yonhap)