US Secretary of State John Kerry held talks in Seoul Thursday on curbing North Korea's nuclear programme, as the two Koreas locked horns at rare, high-level talks over looming South Korea-US military drills.

South Korea was Kerry's first stop on an Asia tour that will also take him to China and Indonesia, with a focus on regional tensions stoked by China's territorial claims.

"North Korea -- obviously the challenge with their nuclear programme -- remains an essential security issue," Kerry said as he met President Park Geun-Hye shortly after arriving.

As well as discussing efforts to rein in Pyongyang's nuclear ambitions, Kerry will be briefed on a diplomatic initiative that saw the two Koreas sit down Wednesday for their highest-level official talks since 2007.

The discussions ran late into the night, and ended without any tangible agreement or joint statement.

But the two sides announced a second round would be held Friday in the border truce village of Panmunjom where the armistice ending the 1950-53 Korean War was signed 60 years ago.

Although the talks have no fixed agenda, the South is focused on ensuring that a planned reunion later this month for family members separated by the 1950-53 Korean War goes ahead as scheduled.

The February 20-25 event overlaps with the start of South Korea's annual joint military exercises with the United States, which Pyongyang has denounced as provocative.

On Wednesday, the North side demanded the joint drills be postponed until after the reunion was over, but the South's Unification Minister Ryoo Kihl-Jae said the request had been turned down.

"The government made it clear this is unacceptable," Ryoo told parliament.

There was no immediate comment from North Korea.

Briefing reporters in Seoul, presidential spokesman Min Kyung-Wook indicated that the talks were a good opportunity for the two rivals to sound each other out.

"We've become clearly aware of North Korea's intentions, and this was also an opportunity for us to clearly explain our principles," he quoted a government official as saying.

- Kerry to seek China pressure on North Korea -

North Korea and its main ally China want a resumption of six-party talks on the North's nuclear weapons programme, but Washington and Seoul both insist that Pyongyang must first demonstrate some tangible commitment to abandoning nuclear weapons.

In Beijing, Kerry will encourage China to "use its unique set of ties and leverage" to pressure Pyongyang to prove it is serious about wanting to restart the six-party process, a State Department official said.

Kerry believes "the North Korean nuclear threat is not a problem that we can all admire from a distance," the official added.

His visit comes ahead of an Asia tour in April by President Barack Obama, which will take in Japan and South Korea.

The US is currently working to secure the release of Kenneth Bae, a Korean-American missionary who was sentenced to 15 years' hard labour in North Korea last year on sedition charges.

The State Department on Tuesday again voiced frustration at Pyongyang's decision to rescind an invitation to US envoy Robert King to discuss Bae's case.

US officials called on North Korea to show "compassion" for the 45-year-old, who is forced to work 10 to 12 hours a day even though his health is failing.

President Park came to office a year ago promising greater engagement with Pyongyang, and Wednesday's high-level talks had raised hopes that the two sides might be ready to embark on a genuine trust-building dialogue.

But South Korea remains wary of the impoverished North's intentions, suggesting that Pyongyang's only real desire is to see the resumption of several lucrative cross-border projects.

Paik Hak-Soon, an analyst at the Sejong Institute in Seoul, stressed there was still room for optimism.

"At least these senior officials met for the first time in a very long time," Paik said.

"You can't expect them to produce a major decision at the first meeting. They go back to the capitals, talk with their leaders," he added.