BEIJING (Reuters) - North Korea must halt its nuclear weapons program now to show it is taking negotiations on disarmament seriously, the chief U.S. negotiator said on Thursday on the second day of six-party talks in Beijing. But North Korean delegates were quoted by a source close to the talks as saying they had no "will" to negotiate with the United States, Japan's Kyodo news agency said. Negotiators said the three-day talks due to end on Friday would focus on the logistics of further bargaining after a framework for disarmament was agreed in September. But the perennial issue remains trust between the two main protagonists, Washington and Pyongyang. "The time for them to stop producing nuclear material is now," chief U.S. negotiator Christopher Hill told reporters. "The faster they move, the faster we move, the faster everybody moves, and I think the faster the DPRK can be reintegrated into the world," Hill said, referring to Pyongyang by its official name, the Democratic People's Republic of Korea. Hill said he would contemplate traveling to North Korea if it would help the talks. Earlier in the day, Hill said: "You know how you build up trust? You live up to the agreement ... You can build up trust through actions." Kyodo quoted unidentified sources as saying North Korea had no will after protesting against various American moves, including freezing assets under U.S. jurisdiction of eight North Korean entities in October. U.S. Ambassador to South Korea Alexander Vershbow said on Wednesday the United States would be willing to open an office in Pyongyang as a gesture of goodwill, but Hill stressed that goodwill should be reciprocal. "The point the U.S. ambassador to South Korea was making was that the DPRK has to establish a level of trust. They're often fond of talking of our level of trust but they have some responsibilities themselves," he said. South Korean envoy Song Min-soon said the six parties -- the two Koreas, the United States, Japan, Russia and host China -- were working to come up with a plan to shut down Yongbyon, the center of the communist state's nuclear programs about 100 km (60 miles) north of the capital, Pyongyang. "What we are negotiating is how to suspend the operation of (the North's) nuclear facility and to accelerate the process of moving toward dismantlement," he told reporters. The United States says the plant has continued to operate since the September 19 joint statement, in which North Korea agreed to dismantle its nuclear programs in exchange for aid and security guarantees. The agreement was seen as a breakthrough, but tough questions remain over the timing of concessions and the North's demands for a light-water reactor for atomic energy. The U.S. says the North cannot receive the reward of a light-water reactor until it has disarmed and opened to nuclear inspectors. Japan's envoy, Kenichiro Sasae, said North Korea had made clear commitments in the agreement and now had to show it would live up to them, for example, by giving a timeline for dismantling its nuclear programs. "North Korea should wipe out suspicions it is playing for time," the Japanese embassy in Beijing quoted Sasae as saying. Despite the hurdles, Hill described the atmosphere on the second day as "fairly businesslike ... (but) too short to be working out a complete implementation plan." Chinese Foreign Ministry spokesman Liu Jianchao called the talks "practical and positive." As host, China's chief negotiator Wu Dawei would likely issue a chairman's statement on the final day on Friday, Hill said. The six-party talks began in 2003 when China sought to broker a peaceful compromise after the United States accused North Korea of covertly building atomic weapons and Pyongyang pulled out of the Non-Proliferation Treaty. The North said in February it had nuclear weapons.