U.S. Secretary of State Mike Pompeo said Monday he is likely to make yet another visit to North Korea "before too terribly long" to follow up on last week's first-ever summit between the two countries.

Speaking at an event in Detroit, Pompeo said there is a great deal of work to do to flesh out an agreement U.S. President Donald Trump and the North's leader Kim Jong Un struck in their historic encounter on June 12 in Singapore.

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"I'll likely travel back before too terribly long," Pompeo said. "We still have to flesh out all the things that underlay the commitments that were made that day in Singapore."

Pompeo, however, said it is "hard to know" whether there will need to be a second summit between Trump and Kim.

Pompeo traveled twice to Pyongyang recently to lay the groundwork for the Trump-Kim summit.

In a joint statement issued after the summit, Kim reaffirmed his "firm and unwavering commitment to complete denuclearization of the Korean Peninsula," while Trump committed to provide security guarantees to North Korea.

Kim promised to "fully denuclearize his country," Pompeo said, adding, "It's not just the weapons system, it's everything."

In return, Trump committed to making sure that the United States and North Korea "alter the armistice agreement," along with South Korea and China, and provide security assurances Kim needs, according to the chief U.S. diplomat.

Pyongyang has been calling for replacing a Korean War armistice with a peace treaty to formally end the 1950-1953 conflict.

The armistice -- signed by the U.S.-led United Nations Command, North Korea and the Chinese People's Volunteer Army -- has left the main combatants technically in a state of war.

In telephone talks Sunday, Pompeo and South Korean Foreign Minister Kang Kyung Wha reaffirmed the goal of complete, verifiable and irreversible denuclearization, the State Department said Monday.

Pompeo and Kang agreed to maintain pressure on Pyongyang until it denuclearizes, it said.