SEOUL, South Korea — North Korea pressed its demand on Friday that the United States agree to declare an end to the 1950-53 Korean War, as South Korea’s leader indicated that the American secretary of state, Mike Pompeo, was preparing for his fourth visit to the North.

Mr. Pompeo, the point man in President Trump’s efforts to end North Korea’s nuclear weapons program, has been struggling to follow up on the agreement reached between Mr. Trump and North Korea’s leader, Kim Jong-un, when they met in Singapore in June in the first summit meeting between their nations.

In Singapore, Mr. Kim committed to work toward the “complete denuclearization of the Korean Peninsula.” But the summit agreement lacked details on how to achieve that goal, and Mr. Pompeo and his team of negotiators has strained since then to win concrete action on this front from their North Korean counterparts.

When he met with representatives of political parties in Seoul on Thursday, President Moon Jae-in of South Korea said that negotiations between the United States and North Korea have recently gained “speed,” with Mr. Pompeo planning to visit North Korea again, according to Yun So-ha, an opposition leader, who briefed reporters on the meeting.