U.S. Secretary of State Mike Pompeo said Monday that he and North Korean leader Kim Jong Un made "significant progress" toward an agreement for the North to give up its nuclear weapons.

Over the weekend, Kim and Pompeo held a productive meeting where they apparently discussed a second summit between Kim and President Donald Trump.

Without getting into specifics, Pompeo also said that Kim had agreed to allow international inspectors at one of North Korea's main nuclear facilities into the country's nuclear a missile sites — a big move towards denuclearization.

"It's a long process," Pompeo told reporters in the South Korean capital of Seoul where he traveled after meeting with Kim in Pyongyang on Sunday. "We made significant progress. We'll continue to make significant progress and we are further along in making that progress than any administration in an awfully long time."

Trump, tweeting from Washington shortly after Pompeo left North Korea, cited progress Pompeo had made on agreements he and Kim came to at their June meeting in Singapore and said, "I look forward to seeing Chairman Kim again, in the near future.′

Pompeo said he and Kim had gotten "pretty close" to fixing the logistics for the summit but stressed that "sometimes that last inch is hard to close."

"Most importantly, both the leaders believe there is real progress that can be made, substantive progress that can be made at the next summit and so we are going to get it at a time that works for each of the two leaders and at a place that works for both of them," he said. "We are not quite there yet. But we will get there."

North Korea's state-run news agency KCNA, meanwhile, said Monday that Kim had "expressed his will and conviction that a great progress would surely be made in solving the issues of utmost concern of the world and in attaining the goal set forth at the last talks with the projected second DPRK-U.S. summit talks as an occasion." DPRK is the acronym for the country's official name: Democratic People's Republic of Korea.

In an early Monday dispatch, KCNA called the talks "productive and wonderful" and said that "mutual stands were fully understood and opinions exchanged."

In Seoul, Pompeo said Kim is expected soon to name deputy foreign minister Choe Son Hui as a counterpart for his new special envoy for North Korea, former Ford executive Stephen Biegun, who accompanied him on the trip. He and Biegun both said they expected meetings at the working level to begin soon and become quite frequent before the next summit.

"We are starting to see a first wave of actions we can take on all four pillars of the Singapore communique," said Biegun, who will serve as Pompeo's pointman in negotiations with the North as well as work with South Korea, Japan, China, Russia, and other countries that have an interest in the talks.