“And the location is important. But there are many conditions that play into that. How long is it going to go on? When you say where, like really where? Not just a city or a country, but like really where?” Mr. Pompeo said. “So we’re trying to put some more meat on that.”

Also, according to a senior aide to South Korea’s president, Moon Jae-in, Mr. Pompeo was expected to leave Pyongyang with three Americans now imprisoned in North Korea and return to the United States with them. All of them are Korean-Americans and all have the surname Kim, although they are not related.

But on Tuesday night, the White House took a more cautious tone, declining to confirm the reports out of South Korea that the Americans were to be released.

Sarah Huckabee Sanders, the White House press secretary, said in a brief interview that arranging the summit meeting remained Mr. Pompeo’s top priority for the visit, and she stressed that the release of the prisoners was “not a done deal.”

Asked whether he expected the North Koreans to release the three detainees to him, Mr. Pompeo said, “I think it’d be a great gesture if they would choose to do so.” And asked whether a summit meeting were possible if the North Koreans continued to detain the Americans, he said, “We’re hopeful we don’t have to cross that road.”

Mr. Pompeo also stressed, as he has done on almost every occasion when publicly speaking about the summit meeting between Mr. Trump and Mr. Kim, that the United States would not support a proposal by President Moon Jae-in of South Korea for step-by-step measures, in which the North Koreans would get sanctions lifted over a period of years as they gradually unwound their nuclear program.

Many analysts in South Korea and around the world believe that such an all-or-nothing strategy will fail with the North Koreans, but a senior administration official traveling with Mr. Pompeo pointed out that previous administrations had tried incremental measures, all of which failed to halt the country’s progress toward building a nuclear arsenal and the missiles to deliver them.

The senior official said that Mr. Kim promised as recently as New Year’s Eve that the country would mass produce nuclear warheads and the means to deliver them, and that a year ago he had ordered the assassination of his half brother with the use of a chemical weapon. One goal of the trip, the official said, was to see whether the North was ready to take the steps needed to prove it had moved beyond such talk and actions.