Rather, Kim said Saturday that "under the proven condition of complete nuclear weapons, we no longer need any nuclear tests, mid-range and intercontinental ballistic rocket tests, and that the nuclear test site in northern area has also completed its mission", according to CNN, which cited North Korea's state-run news agency.
North Korean leader Kim Jong-un invited Trump to a summit in March as he expressed a commitment to denuclearize and to suspend all nuclear and ballistic missile tests.
The communist country also says it is also shutting down the Poongye-ri nuclear test site where six underground tests have taken place. But Pyongyang called Kim's declaration "completion of weaponization of nuclear weapons" and "an important step toward global nuclear weapons reduction".
Trump nonetheless tweeted Sunday that the North has "agreed to denuclearization (so great for World), site closure, & no more testing!"
He added on ABC's "This Week" that it's unrealistic to think that "somebody's going to go in and charm" Kim out of keeping his nuclear weapons.
The Clinton administration reached a major nuclear agreement with Pyongyang in October 1994, ending months of war fears triggered by North Korea's threat to withdraw from the nuclear Non-Proliferation Treaty and convert its stockpile of nuclear fuel into bombs.
One Palestinian killed, two injured in overnight air strikes in Gaza
Friday prayers will be held outside the tents, which were erected 700 hundreds of meters away from the fence of the border. The IDF General Staff has ordered an investigation into the Israeli military's response to the Gaza border protests.
Sunday's comments followed those from Trump on Friday after Kim pledged to halt nuclear testing in what was seen as a largely symbolic gesture aimed at softening the ground for talks between the two leaders. "He saw what happened with Gaddafi".
North Korea has defended its nuclear and missile programmes as necessary deterrents against perceived USA hostility.
"We will concentrate all efforts on building a powerful socialist economy and markedly improving the standard of people's living through the mobilization of all human and material resources of the country", the KCNA said.
Trump said last week Washington was negotiating for the release of the men and there was "a good chance of doing it". It has conducted numerous missile tests, and past year it detonated its most powerful nuclear bomb.
On Monday, the two Koreas will hold another round of working-level talks at the Tongil Pavilion on the North Korean side of Panmunjom to discuss protocol, security and media coverage of the summit. Halting its nuclear activity would not only bring Chinese money back to the country but would open North Korea to a whole range of new business opportunities.
"Well, I think this announcement on Friday is better than continued testing, but it's not much better than that", he said.