South Korean President Jae-in Moon accepted the offer for bilateral talks with the blessing of President Trump.
It added: 'The anti-Trump book is sweeping all over the world so Trump is being massively humiliated worldwide'. "I like it very much what I am seeing", Trump told reporters at the White House on Wednesday.
There were also talks of carrying out a limited strike on North Korea with the fears of a nuclear war in the background.
"We have certainly problems with North Korea", Trump said at a news conference. "I think you people are surprised", said the US President.
The South Korean president noted on Wednesday that U.S. President Donald Trump was important in helping to bring about conditions that permitted the negotiations. The two sides also agreed to hold military talks in an attempt to prevent an accidental conflict on the peninsula.
North Korea has become Trump's most urgent foreign crisis, as he struggles to contain the regime's rapidly advancing nuclear weapons and ballistic missile programs. North Korea has a massive array of artillery pieces pointed at Seoul, South Korea's capital of with a population of 25 million.
Trump has mocked Kim's weight and called him "little rocket man" in a speech to the United Nations General Assembly.
Trump also told Moon that Vice President Mike Pence and his wife Karen Pence will lead the US delegation to the Winter Olympics, scheduled for February 9-25 in Pyeongchang.
Moon and Trump agreed to continue a "maximum pressure campaign" against Pyongyang, the White House said in its statement. North Korea previous year increased the pace of its missile programme.
Diplomats from other Western countries also welcomed contacts between Pyongyang and Seoul but did not support the idea of easing the sanctions against North Korea.
Kim warned he had a nuclear button on his desk and the "entire mainland of the U.S. is withing the range of our nuclear weapons".
He welcomed them, but warned that his country would continue to work with the global community to apply pressure on the North to give up nuclear weapons.