New US Secretary of State Mike Pompeo also said he had a 'good conversation' with Kim during his visit to Pyongyang, adding he was 'prepared to... lay out a map that would help us achieve' denuclearisation.
South Korean President's office says Kim promised to close N Korea's nuclear test site next month.
United States President Donald Trump on Saturday suggested that a meeting between the US and North Korea is likely possible in 'three or four weeks'.
"We'll have a meeting over the next three or four weeks," CNN quoted Trump as saying during a rally in Michigan, which he is holding on the night of the White House Correspondents' Dinner, as he skips the annual bash for second consecutive year.
According to the report, earlier on Saturday, Trump spoke with South Korean President Moon Jae-in earlier and mentioned in his speech that the South Korean leader credited him for the apparent progress with North Korean leader Kim Jong-un.
"He gives us tremendous credit. He gives us all the credit," Trump said.
Meanwhile, Moon's office said on Sunday that Kim said during Friday's summit that he would close the country's nuclear test site next month.
"Kim said during the summit... that he would carry out the closing of the nuclear test site in May," Moon's spokesman told reporters.
This comes in the backdrop of North Korean leader Kim Jong-un and South Korean President Moon Jae-in ending their historic summit on Friday with a glimmer of hope and positivity in Panmunjom.
New US Secretary of State Mike Pompeo also said he had a ‘good conversation’ with Kim during his visit to Pyongyang, adding he was ‘prepared to... lay out a map that would help us achieve’ denuclearisation.
Pompeo made the remarks in an exclusive interview with ABC News, extracts of which were released ahead of its broadcast on Sunday.
Trump also said that the world went from having a potential disaster, but the Olympics and North Korea's participation helped to turn things around, according to the reports.
To begin with, Kim became the first-ever North Korean leader to step on the South Korean soil, when he took a step at the border village of Panmunjom in the Demilitarised Zone, the world's most heavily guarded border, separating the two countries. He then shook hands with Moon, which was the first-ever meeting between them after the Korean War ended in 1953.
The inter-Korean summit was also unique as it was the first time in over a decade that it was being held. The previous two summits were held in 2000 and 2007 in Pyongyang.
It was also the first time that the summit was being held in South Korea.
The Korean War between the two countries took place between 1950-53, which ended with a ceasefire and signing of an armistice agreement.
Technically, both the countries are still at war since no peace treaty has been signed between them.
In a joint declaration after the talks, the two leaders officially inaugurated a document formally called the 'Panmunjom Declaration for Peace, Prosperity and Unification on the Korean Peninsula.'
The declaration read, "The two leaders solemnly declare that there will be no more war on the Korean Peninsula and a new era of peace has begun," CNN reported.
The two Koreas agreed to sign a peace treaty formally later this year, ending the six-decades-old war between the two countries.
Moon also reiterated that it marked the rise of 'a new era of peace'.
The South Korean President is also slated to visit Pyongyang later this year, according to a statement released by his presidential office.
Many countries such as China, Russia and Japan and the United Nations (UN) have praised the outcome and positivity of the successful summit.
They hoped for ending of hostilities and pressing for peace, denuclearisation and reconciliation of the Korean Peninsula.
With inputs from PTI