Secretary of State Mike Pompeo says that the president anticipates making the case in his second address to the United Nations General Assembly that "now is not the time to ease pressure" on North Korea as the administration continues its "maximum pressure" campaign until complete and verifiable denuclearization is achieved.
Mr. Trump earlier on Monday told reporters that that a second meeting with North Korean dictator Kim Jong Un would be taking place "quite soon."
"Kim Jong Un wrote a letter, a beautiful letter, asking for a second meeting, and we will be doing that. Secretary Pompeo will be working that out. In the immediate future, it looks like it's moving very well," the president said.
At, Mr. Trump said that the North risked "total destruction" if it continued to pursue nuclear weapons, and he said of Kim, "Rocket Man is on a suicide mission for himself and his regime."
Pompeo would not confirm to reporters at Monday's briefing the timeline for when such a summit would take place, but said, "Lord willing, I'll be traveling before the end or the year," to continue discussions with his counterparts in Pyongyang.
Pompeo said while he's optimistic North Korea will make good on its pledge to denuclearize, it would be "foolish" to set a certain date for how long the U.S. will leave the door open for talks with North Korea.
"Make no mistake, the conversations are important, they're putting the opportunity to complete the denuclearization in place. We'll continue at every level to have those conversations," he said. Pompeo added that there remains work to be done in the region and that it will be "some time" before complete denuclearization takes place.
North Korea has indicated in discussions with South Korea that it is willing to make additional concessions beyond closing some launching and testing facilities only if the U.S. will declare an official end to the Korean War by the end of the year.
This year's General Assembly will be Mr. Trump's second meeting since taking office and Pompeo's first since taking over as secretary of state.
CBS News' Errol Barnett contributed to this report.