The UN chief has "saluted the courage and leadership" that resulted in yesterday's pledges by Korean leaders
North Korean state media has described the summit between North and South Korea as 'historic'.
On Friday, the North's leader Kim Jong Un crossed the South Korean border at the demilitarised zone (DMZ) for the first summit between the two countries in more than a decade.
After several hours of talks, Mr Kim and South Korean President Moon Jae In signed a joint declaration pledging to achieve a "nuclear-free Korean Peninsula".
They also declared their intention to formally end the war between the two countries this year.
The two countries have been separated since 1953, when an armistice was signed to bring an end to the fighting in the Korean War.
In comments quoted by Reuters, North Korea's KCNA news agency said: "At the talks both sides had a candid and open-hearted exchange of views on the matters of mutual concern including the issues of improving the north-south relations, ensuring peace on the Korean Peninsula and the denuclearisation of the peninsula."
State television is also reported to have broadcast footage of the summit.
World leaders have given a cautious welcome to the apparent progress made during the Korean summit.
A spokesperson for UN Secretary General Antonio Guterres said: "Many around the world were moved by the powerful imagery of the two leaders coming together to advance harmony and peace on the Korean Peninsula.
"The Secretary-General salutes the courage and leadership that resulted in the important commitments and agreed actions outlined in the Panmunjom Declaration for Peace, Prosperity and Unification of the Korean Peninsula."
The statement adds: "He counts on the parties to build on their first meeting and swiftly implement all agreed actions to further inter-Korean trust-building and reconciliation; sincere dialogue; and progress towards sustainable peace and verifiable denuclearization on the Korean Peninsula."
Before the summit, UN Special Rapporteur Tomás Ojea Quintana warned that the issue of human rights abuses in North Korea must be a key focus in any peace talks - saying ignoring it in the first round of negotiations would be a "misstep and lost opportunity".
The US, meanwhile, has said the summit is just 'one step' towards denuclearisation - with Vice President Mike Pence saying any promises from North Korea "will be met with reservation, vigilance, and verification".
Donald Trump - who is planning to meet Mr Kim in the coming months - said the US would 'maintain pressure' on North Korea.
However, he also told reporters: "It’s never gone this far. This enthusiasm for them wanting to make a deal ... We are going to hopefully make a deal."