The historic meeting between Mr Trump and Kim Jong-un would be the first between sitting U.S. and North Korean leaders. The officials were sent to Washington to hand-deliver a letter from Kim Jong-un to the US president.
The key meeting, scheduled for 12 June, has been jeopardised so far by belligerent statements from North Korea and threats of cancellation from Mr Trump. "It went very well", President Trump told reporters on the White House lawn.
Kim Yong Chol, the North Korean leader's top aide, is the highest-ranking North Korean official to visit the U.S. in 18 years, and his trip to the White House will be a highly symbolic sign of easing tensions after fears of war escalated amid North Korean nuclear and missile tests last year.
"I look forward to seeing the letter and I look forward to June 12 where hopefully we can make progress", Trump said.
Trump said he believed Kim Jong Un would agree to denuclearization. Nothing will be signed on June 12, Trump said. How much? How much?
Washington wants North Korea to quickly give up all its nuclear weapons in a verifiable way in return for sanctions and economic relief.
He said Moscow hoped all sides would take a measured approach to possible forthcoming talks on a nuclear settlement.
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Mattis' comments drew a pointed reaction from a Chinese official at the meeting. President Donald Trump on Friday said the summit will take place June 12.
Singapore, a small but wealthy Southeast Asian city-state, is determined to successfully host the summit and is willing to foot at least some of the bill.
It was an extraordinary change in tone from a president who past year threatened to rain "fire and fury like the world has never seen" on North Korea because of the threat its nuclear weapons and missiles posed to the United States. Hours later, Trump said the summit was potentially back on. About eight minutes later, Trump said he not only hasn't read the letter yet, but he also never opened the envelope.
He added that much of the diplomacy must also be assisted by the DPRK's regional neighbors like South Korea, Japan and China.
Kim Yong Chol's trip to Washington was clearly a response to U.S. Secretary of State Mike Pompeo's travelling to Pyongyang, North Korea's capital, twice in recent weeks for pre-summit negotiations with Kim.
"It is an ironic and telling deviation from North Korea's insistence on being treated on an 'equal footing, '" Scott Snyder, a Korea expert at the Council on Foreign Relations, told the paper.
The fate of the much-anticipated summit on the Korean nuclear crisis seemed sealed a week ago, after Trump stunned the worldwide community by saying that he'd cancelled the talks with Kim, due to some "tremendous anger and open hostility" in Pyongyang's statements. But North Korea flipped on the United States in May, blasting Trump officials and saying it was reconsidering the summit. "Remember what I say: We will see what we will see".