President Moon Jae-in and United States President Donald Trump have agreed to continue close consultation to ensure the upcoming U.S.-North Korea summit will reach an agreement on concrete measures to denuclearize North Korea.

The presidential office said Sunday that the two leaders reached the agreement during a telephone conversation on Saturday, which lasted for 75 minutes from 9:15 p.m.

The top office said that the leaders discussed the outcome of Moon's historic summit with North Korean leader Kim Jong-un held Friday at the border truce village of Panmunjeom.

Trump reportedly offered his congratulations over the successful summit and hailed the two Korean leaders' affirmation of a shared goal of complete denuclearization of the Korean Peninsula.

Moon and Trump also agreed on the need to hold the U.S.-North Korea summit as soon as possible to keep the momentum of the successful inter-Korean summit.

The two leaders also reportedly narrowed possible venues for the summit to two to three locations and exchanged views over the pros and cons of the candidate sites.

Trump tweeted on Saturday that he had a "long and very good talk" with Moon, adding his meeting with Kim will likely take place in May or early June.

Trump said that things were going very well and that the time and location of his meeting with Kim were being set, adding that they have now narrowed the possible site of the first-ever U.S.-North Korea summit to two or three countries.

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