With North and South Korea slated to hold another round of direct talks Friday, Secretary of State John F. Kerry praised the two sides for entering into their highest-level engagement in seven years but warned that Washington won’t join the talks until Pyongyang takes “meaningful action” toward denuclearization.

The unexpected round of negotiations, which began Wednesday in a village on the border between the two Koreas, followed a softening of the North’s usual saber-rattling toward the South and Washington, which reached a fever pitch with threats of a nuclear strike in April.

Although the North’s 30-something leader Kim Jong-un softened his posture by expressing interest in better North-South relations during a January speech, Pyongyang embraced an aggressive approach to the talks by demanding that the South reduce its military ties with Washington.

South Korean President Park Geun-hye, who won widespread backing from voters last year by promising to improve relations with the North, participated directly in Wednesday’s talks.

Behind the scenes, U.S. and South Korean officials have remained suspicious that the North’s leader may be more interested in diverting attention from his nation’s nuclear advancements than achieving any lasting reconciliation with the South.

Mr. Kerry appeared to have such concerns on his mind Thursday during a visit to South Korea, where he dismissed the North’s demands that the South back out of upcoming annual military exercises with the U.S.

He also stressed that Washington is “ready and able to deter North Korean aggression.”

Despite long-standing disapproval from the U.N. Security Council, North Korea has conducted nuclear weapons tests in recent years and in April made repeated threats to carry out a nuclear strike against the U.S. mainland.

“Let me be clear,” Mr. Kerry said after a meeting with South Korean Foreign Minister Yun Byung-se in Seoul. “The United States will not accept North Korea as a nuclear-armed state.”

Mr. Kerry also said that while Washington supports the North-South meetings, the U.S. “will not accept talks for the sake of talks.”

The North, he added, has a long track record of skirting obligations to the international community to abandon its nuclear weapons program and must “show that it will live up to its commitments.”

Aside from the nuclear issue, the remark could be read as a backhanded response to North Korea’s flip-flop on Kenneth Bae, an American pastor who has been imprisoned by Pyongyang since 2012.

Mr. Bae, who was working as a tour guide in North Korea at the time of his arrest, has been charged with “crimes against the state” and sentenced to hard labor.

Last month, North Korea suddenly allowed a video of an exhausted-looking Mr. Bae to circulate through the world’s media. When the North then invited U.S. envoy Robert King to come and discuss Mr. Bae’s status, hopes surged in Washington that Pyongyang may be nearing a decision to release the American.

Those hopes were dashed when North Korea abruptly canceled the invitation at the start of this week, days before Mr. Kerry arrived in Seoul.

If nothing else, the move served to bump the issue of U.S.-North Korea tensions high onto the agenda of secretary of state’s trip.

In Seoul on Thursday, Mr. Kerry called on South Korea and Japan — widely regarded to be Washington’s closest military allies in the region — to work through their mutual tensions and create a cohesive front on North Korea.

His stop in Seoul was part of an Asian tour that will include meetings Friday in Beijing with high-level Chinese officials, who are seen by the Obama administration as holding the most influence over North Korea.

“No country has a greater potential to influence North Korea,” said Mr. Kerry, who engaged in an intense round of talks with Chinese officials in April as tensions with North Korea were peaking.

As part of his remarks Thursday, Mr. Kerry praised China for helping reduce tensions with Pyongyang.

Some regional analysts, meanwhile, say Mr. Kim may be pursing talks with the South to show China and the U.S. that he is serious about reducing regional tensions, regardless of international concerns over the North’s nuclear activities.

According to the Reuters news agency, Cheong Seong-chang of the Sejong Institute outside Seoul said that if North Korea is able to show an improvement in relations with the South, “it will mean a better atmosphere for Kim Jong-un to visit China and a justification to pursue high-level talks with the United States.”

No agenda had been arranged when the North-South talks opened Wednesday at the Panmunjom village on the border between the two nations, which have remained divided since the 1950-53 Korean War.

Tensions have run high in recent years, particularly since 2010 amid widespread anger and suspicion in the South that the North had been responsible for a torpedo attack that sank a South Korean warship, killing 46 sailors.

The incident seems unlikely to come up during this week’s talks, but Reuters cited a South Korean official as saying a range of issues were discussed.

Particular emphasis was placed on a plan to allow reunions of families that have been split between the two Koreas for more than 60 years.

The two sides previously agreed to allow such reunions at a resort just inside the North next week — an event that many in South Korea consider a major humanitarian breakthrough with the North.

But North Korea has threatened to cancel the reunions over frustration that the South allowed a nuclear-capable U.S. B-52 bomber to fly near the Korean Peninsula.

The U.S. military has 28,500 troops stationed in South Korea, and the North’s state-controlled media have described upcoming U.S.-South Korean military exercises as a rehearsal for war.

• This article is based in part on wire service reports.

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