U.S. Secretary of State Mike Pompeo and a senior North Korean official admitted Saturday that they have things to "clarify," opening a second day of talks in Pyongyang.

Pompeo and Kim Yong-chol, vice chairman of the Central Committee of the Workers' Party of Korea, met with each other for nearly three hours Friday apparently on details of what the two countries should do in order to implement the Singapore summit deal last month.

Kim told the secretary, "We did have very serious discussion on very important matters yesterday. So, thinking about those discussions you might have not slept well last night," according to news reports based on pool notes.

Several reporters are accompanying Pompeo on his third trip to Pyongyang in as many months aimed at fleshing out the June 12 Singapore accord between President Donald Trump and the North's leader Kim Jong-un, during which Kim agreed to the "complete" denuclearization of Korea in return for security guarantees.

Pompeo said he "slept just fine."

The North's official also said, "There are things that I have to clarify," and Pompeo responded, "There are things that I have to clarify as well."

What they meant was not immediately confirmed.

The secretary reminded the North's official, known as a right-hand man of leader Kim Jong-un, of President Donald Trump's talk of a "brighter future for North Korea" in case of its full denuclearization.

Earlier in the day, State Department spokeswoman Heather Nauert told reporters that the two sides have established working groups to talk about details of a denuclearization plan.

Pompeo is leading an inter-agency team of officials on the trip, which includes Sung Kim, the department's well-known Korea expert.

He arrived in Pyongyang on Friday for a two-day stay. He's expected to meet with the North's leader, but no schedule has been confirmed yet.

He had meetings with Kim on his two previous trips to Pyongyang that helped lay the groundwork for the summit.

Nauert said the North's plan to repatriate the remains of some American troops killed in the 1950-53 Korean War was discussed in the first day's session.

If realized, it's another goodwill gesture by the North to follow up on the Singapore agreement.

What's drawing keen attention is whether the two sides will reach an agreement on a timeline and a method for denuclearization.

The North's media belatedly reported the secretary's arrival there.

A U.S. delegation led by Pompeo is to "take part in the first DPRK-U.S. high-level talks for implementing the joint statement adopted and made public at the DPRK-U.S. summit meeting and talks," the state-run Korean Central News Agency said in a two-paragraph report on Saturday morning.

It gave no other information. The DPRK stands for the North's official name, the Democratic People's Republic of Korea.

Before landing in Pyongyang, Pompeo said, "On this trip, I'm seeking to fill in some details on these commitments and continue the momentum toward the implementation of what the two leaders promised each other and the world.

"I expect that the DPRK is ready to do the same," he said.

He said he was looking forward to "continuing our work toward the final, fully verified denuclearization of #DPRK, as agreed to by Chairman Kim."

The U.S. hopes to maintain momentum amid news reports, based on U.S. intelligence sources, that the secretive North is continuing its nuclear activity. Many of them point to indications of a build-up of the regime's nuclear-related facilities and accuse Pyongyang of trying to deceive Washington in order to extract concessions.

U.S. National Security Adviser John Bolton said Sunday that he expects Pompeo to discuss with the North Koreans a plan to dismantle the nuclear weapons and ballistic missile programs in a year.

In possible pursuit of a more realistic goal, the Trump administration has started to use the term "final, fully-verified dismantlement (FFVD)" of the North's nuclear program instead of the "complete, verifiable and irreversible denuclearization (CVID)" jargon that Pyongyang apparently loathes.

Nauert denied that the administration has eased its demands.

"Nothing could be further from the truth. Our policy toward North Korea has not changed," she was quoted as telling reporters en route to Pyongyang.

Pompeo will fly straight to Tokyo from Pyongyang to brief his South Korean and Japanese counterparts -- Kang Kyung-wha and Taro Kono -- on the outcome of his meetings in North Korea. (Yonhap)