US Secretary of State Mike Pompeo held talks in North Korea for the second on Saturday as he sought “clarity” on the parameters of an agreement to denuclearize the Korean Peninsula. On his third trip to Pyongyang since April and his first since last months historic summit between President Donald Trump and North Korean leader Kim Jong Un, Pompeo was meeting Kim Yong Chol, a senior ruling party official and former spy agency chief. Both men said they needed to "clarify" certain elements of their previous discussions, but provided no detail. Kim Yong Chol said at the start of Saturday’s meeting that the two had had “very serious discussion on very important matters yesterday”. Pompeo reiterated that Trump was “committed to a brighter future for North Korea”. “So the work that we do, the path toward complete denuclearization, building a relationship between our two countries, is vital for a brighter North Korea and the success that our two presidents demand of us,” Pompeo said. Kim agreed that the work was important. “There are things that I have to clarify,” he said. Pompeo responded: “There are things that I have to clarify as well.” The two sides have been struggling to specify what exactly "denuclearization" would entail and how it could be verified to the satisfaction of the United States. A meeting between Pompeo and Kim Jong Un later Saturday was expected but not certain, US officials said. US State Department spokeswoman Heather Nauert said Pompeo had been “very firm” on three basic goals: the complete denuclearization of North Korea, security assurances, and the repatriation of US remains from the 1950-53 Korean War. “He’s spoken about every element of the agreement from Singapore,” she told reporters, according to a pool report from Pyongyang. She said there had been no softening in the US positions, although she would not explain why the department no longer defines its aim as “complete, verifiable, irreversible denuclearization” (CIVD). “Our policy hasn’t changed,” she said several times when asked about CVID. “Our expectation is exactly what the president and Kim Jong Un jointly agreed to in Singapore, and that is the denuclearization of North Korea.” Kim Jong Un made a broad commitment to “work toward denuclearization of the Korean Peninsula” in Singapore but offered no details of how or when North Korea might dismantle a weapons program that Trump has vowed will not be allowed to threaten the United States. Trump, meanwhile, committed to providing “security guarantees” to North Korea and Washington later called off one of its major joint military exercises with South Korea, which Pyongyang regularly denounces as rehearsals for invasion. Nauert said US and North Korean officials had set up working groups to deal with “nitty gritty stuff”, including verification of efforts to achieve denuclearization, which would be headed on the US side by Sung Kim, a Korean-American who is also ambassador to the Philippines. Pompeo held nearly three hours of talks with Kim Yong Chol on Friday and a working dinner that Nauert described as further “relationship building”. She said the dinner lasted an hour and 45 minutes and at times the two were “cracking jokes” and “exchanging pleasantries”. North Korea’s official KCNA news agency said Pompeo’s delegation was taking part in high-level talks for implementing the Singapore summit statement but gave no more details. Pompeo’s talks will be closely watched in the region. He is due to meet officials from allies South Korea and Japan in Tokyo on Sunday. He will then travel to Vietnam and the United Arab Emirates before heading to Belgium, where he will accompany Trump at the NATO summit in Brussels.