U.S. -North Korea relations are "very good" and "the process is moving along", Trump added. On Tuesday, Trump attempted to clean up the controversy when he said he had misspoken during the news conference and affirmed that he has "full faith and support for America's intelligence agencies".
US Secretary of State Mike Pompeo also seems to be in favor of a fast denuclearization process.
Last week North Korea accused the U.S. of making "gangster-like" demands for the process, and branded the USA attitude at high-level talks as "extremely troubling".
Trump announced after the June summit that Kim had agreed to return the remains of "thousands and thousands" of Americans killed in the Korean War, but no remains have been handed over since then, raising further questions about North Korean intentions.
The president's latest comments on the timeline for denuclearisation appear to shift from his position ahead of the summit with Mr Kim, when he said denuclearisation should start "without delay".
Woman survives for a week after crashing vehicle off 200-foot cliff
She was rushed to a nearby hospital by helicopter. "Reports are she was talking and could walk", according to the statement. An Oregon woman who vanished last week in California has been found injured after her Jeep went over a cliff near Big Sur.
As tensions between North Korea and the United States rose in 2017, senior diplomats and administration officials in Washington said diplomacy with North Korea was an option. The gathering came after Pyongyang demolished tunnels leading to its underground nuclear testing site.
It was the first time in nine years that USA and North Korean generals held talks. The two Korean countries are still technically at war, although Moon and Kim had pledged at the inter-Korean summit that they will sign a peace treaty to end the six-decade Korean War formally.
"(North Korea) for decades told their own people that without nuclear weapons their country was at risk of being attacked by the West, by America, by some other country", Pompeo explained.
According to Yonhap, the two mixed doubles teams of Choe Il (North Korea)-Yoo Eun-chong (South Korea) and Jang Woo-jin (South Korea)-Cha Hyo-sim (North Korea) qualified for the last-16 of the International Table Tennis Federation (ITTF) World Tour event in South Korea's Daejeon city.