A handout photo made available by the U.S. State Department shows U.S. Secretary of State Mike Pompeo briefing the press and taking questions about the upcoming trip prior to departing for Saudi Arabia from Andrews Air Force Base, Maryland, the U.S., June 23. EPA-Yonhap

U.S. Secretary of State Mike Pompeo has said there may be a "very real possibility" of Washington and Pyongyang resuming their working-level nuclear talks, after their leaders have exchanged personal letters.

According to the State Department, Pompeo also said in his remarks to the press on Sunday (Washington time) that the United States is prepared to engage in dialogue with the North at a "moment's notice" should the North indicate it is ready.

The remarks came hours after the North's state media reported that leader Kim Jong-un had received a personal letter with "excellent and interesting content" from U.S. President Donald Trump. Earlier this month, Trump also got a letter from Kim, which he called "beautiful" and "very warm."

"We have been working to lay the foundations for that since Hanoi. We think we're in a better place, and I think the remarks you saw out of North Korea this morning suggest that that may well be a very real possibility," Pompeo said when asked about the possibility of working-level talks with the North recommencing in the near future.