Secretary of State Mike Pompeo said Friday the United States is preparing for a second summit between President Donald Trump and North Korean leader Kim Jong Un, and that there is still work to do before it happens.

"There's still a little bit of work to do to make sure that the conditions are right and that the two leaders are put in the position where we could make substantial progress" toward the denuclearization of North Korea, Pompeo said in an interview with Fox News.

"I'm hoping I'll be back in Pyongyang before too long to make some more progress," he said. "And if that's the case, I'm very hopeful that Chairman Kim and President Trump will get a chance to meet in the near future as well."

(Mike Pompeo)[Getty/Kyodo]

Pompeo did not say when and where he thinks the second meeting between Trump and Kim, chairman of the Workers' Party of Korea, will take place following the first-ever U.S.-North Korea summit in June in Singapore.

In a separate interview with NBC News, Pompeo said talks between Kim and South Korean President Moon Jae In earlier this week in Pyongyang represented "important steps" in the effort to denuclearize the Korean Peninsula.

Kim and Moon discussed denuclearization "in a material way" for the first time, he said.

Following the latest inter-Korean summit, the chief U.S. diplomat has invited North Korean Foreign Minister Ri Yong Ho for a meeting next week when the two attend the U.N. General Assembly in New York.

Pompeo has expressed readiness to "immediately" engage in negotiations with North Korea in a bid to achieve the goal of denuclearizing Pyongyang by the end of Trump's first term in January 2021.

Asked about a series of alleged sanctions violations since the Singapore summit, Pompeo told NBC that the U.S. government was working on closing those "gaps."

"There's always gaps," he said. "We're working diligently on enforcement of those Security Council Resolutions and those economic sanctions will remain in place until we get to the end."