"Let me be clear. The US will not accept North Korea as a nuclear state. It will not accept talks for the sake of talks," Xinhua quoted Kerry as saying during a joint press conference with his South Korean counterpart Yun Byung-se.
Kerry's visit came in line with the agreement reached with Yun Jan 7 when the top South Korean envoy went to Washington. At that time, Kerry and Yun agreed to deepen consultations on the North Korea issue. Since then, several US diplomats, including deputy US Secretary of State William Burns, visited Seoul.
"We have yet to see evidence that North Korea is prepared to meet its obligations and negotiate the verifiable denuclearisation of the Korean Peninsula," Kerry said.
To resume the six-party talks, Kerry said that Pyongyang should show its sincerity first toward denuclearisation.
South Korea was the first stop on Kerry's Asian tour, which will also take him to China, Indonesia and the United Arab Emirates (UAE). After wrapping up his schedules, Kerry will fly to Beijing for dialogue with his Chinese counterpart Wang Yi.
Before holding talks with Yun, Kerry paid a courtesy call to South Korean President Park Geun-hye. Their meeting ran for around two hours, longer than earlier scheduled.
During the meeting, Park told Kerry that the reunified Korea will have no nuclear weapons and make an active contribution to regional peace and prosperity, according to the presidential office Cheong Wa Dae.
The first South Korean woman leader said that the reunification will go beyond overcoming the divided Korean Peninsula and will create fresh future and growth engine in Northeast Asia, which will confer great benefits to neighbouring countries.
Kerry appreciated Park's vision of reunification "bonanza", saying it is worth setting a high value on the vision as it went beyond the denuclearisation issue to begin discussions on the future. The bonanza became a buzzword in the country after Park described the future reunification as such in her New Year's speech.
North Korea called on South Korea during the high-level talks held Wednesday at the truce village of Panmunjeom to postpone the South Korea-US military drills until after the family reunion ends later this month.
The first talks between high-ranking officials in around seven years ended without any tangible agreement. The two Koreas will resume the inter-governmental talks Friday at the same venue on the border dividing the Korean Peninsula.
Combined forces of South Korea and the United States will conduct the "Key Resolve" and "Foal Eagle" war games from Feb 24 to April 18, which overlap for two days with the family reunion event. The two Koreas will hold reunion of families separated by the 1950-53 Korean War from Feb 20-25 at the DPRK's scenic resort of Mount Kumgang.
Kerry's visit to Seoul coincided with the announcement of US President Barack Obama's visit to South Korea and Japan in April.