They were expected to exchange their basic positions ahead of what could be another grueling tug of war.

Security was tight on the roads leading to the negotiation venue with police and their vehicles blocking outsiders' access to it, as a throng of foreign journalists and camera staff jostled for position.

The extraordinary level of security appeared to reflect the negotiators' desire to focus on their high-stakes talks without being sidetracked, observers said. 

Shortly after the morning negotiation session, the North's chief delegate Kim tersely said, "Let's see," in response to a reporter's question of whether he is satisfied with the fresh talks.

US Secretary of State Mike Pompeo said that he was hopeful of progress in the latest talks with the North, according to Reuters.

 "I'm hopeful that we will (make progress)," Pompeo told a news conference in Athens, according to Reuters.

"We came with a set of ideas, we hope the North Koreans came with a good spirit and a willingness to try to move forward and implement what President Trump and Chairman Kim agreed to back in Singapore," he added.

Pompeo also noted that still "a lot of work needs to be done."

Swedish Foreign Minister Ann Linde confirmed that the nuclear talks were under way in the European country.

"I am encouraged that US and DPRK working level delegations are currently in Sweden to hold talks," she wrote on Twitter. DPRK stands for the North's official name, Democratic People's Republic of Korea. 

"Dialogue needed to reach denuclearization and peaceful solution," she added.

A day earlier, the countries' deputy delegation chiefs -- Mark Lambert of the US and Kwon Jong-gun of the North -- were said to have had preliminary contact on the outskirts of Stockholm, to discuss administrative issues for the formal resumption of their negotiations. The pre-negotiation session was said to have been "amicable and productive."

The fresh nuclear talks were expected to center on how to make substantive progress in the implementation of the landmark agreement that Trump and Kim reached during their first summit in Singapore in June last year.

The agreement includes a set of their commitments to build new bilateral relations, make joint efforts to build a lasting and stable peace regime on the peninsula and work toward the "complete denuclearization" of the peninsula.

Uncertainty still shrouds the much-anticipated negotiations between Washington and Pyongyang given that they remain far apart over the scope of Pyongyang's denuclearization, its disarmament method and what rewards it will receive in return.

Tangible progress from the negotiations is expected to pave the way for a third summit between Trump and Kim.

 Before the negotiations, the North's delegation chief Kim said he bore "high expectations and optimism."

 In recent weeks, top US officials' statements have also raised optimism about a compromise with Pyongyang.

 Trump has made remarks that hinted he is warming to Pyongyang's call for a "new calculation method," while Secretary of State Mike Pompeo has repeated conciliatory messages, such as there being a "bright future" for a nuclear-free North Korea.

 Citing two US officials, the US magazine Time reported that Trump is prepared to offer Kim a three-year suspension of United Nations sanctions on textile and coal exports if Pyongyang agrees to dismantle its main nuclear facility at Yongbyon and halt its production of highly enriched uranium.

 It also cited one of the officials as saying if the United Nations is not willing to follow Trump's lead, the US could temporarily halt its enforcement of those sanctions.

 The US media outlet, Vox, also reported on such an offer on Wednesday. (Yonhap)