JEJU, South Korea -- The top nuclear envoys of South Korea and the United States reaffirmed Friday that they are seeking a "peaceful" way to resolve North Korea's nuclear stalemate and vowed to keep their joint campaign of pressure to bring Pyongyang to talks on its denuclearization.

The reaffirmation came after Lee Do-hoon, South Korea's special representative for Korean Peninsula peace and security affairs, and his US counterpart, Joseph Yun, met on the southern resort island of Jeju to discuss their coordinated approach towards the North's nuclear and missile threats.

The meeting followed a summit between their leaders -- South Korean President Moon Jae-in and US President Donald Trump -- in Seoul last week.

"There is no doubt that both of the presidents want to find a peaceful way in regard to North Korea's nuclear issue. So we discussed them and we agreed the pressure campaign has to be a central element," Yun told reporters after completing a meeting that lasted for more than a hour.

Yun said that the common policy between Seoul and Washington against the North is to attain its denuclearization and rally global support for putting pressure on the reclusive state to engage in a "meaningful" and "credible" dialogue. 

"We have been engaged with countries like China, Russia, as well as Japan and the EU, aimed at getting pressure on North Korea to have a meaningful and credible dialogue with us so that they can take steps towards the denuclearization," he said. "We very much agree on that, and again today we reaffirmed that goal."

Answering a question seeking comments on a planned visit by Chinese President Xi Jinping's special envoy to North Korea on Friday, Yun hoped that it would help "forward" the goal of its denuclearization. 

"China, of course, has a big role to play on Northeast Asia security issues. I hope, as China has done within the (United Nations Security Council) and elsewhere, it regards the denuclearization as a critical goal. We do hope that special envoy will forward that goal," he said.

Lee also drew more significance from the fact that China will send a special envoy to Pyongyang, saying that South Korea is closely watching what will come out of the visit.

"It could have a very significant meaning considering the current situation," he told reporters. "We will keep an eye on the outcome and meet again (with Yun) as soon as possible to analyze it together."

He noted that the current pressure and sanctions-oriented drive is aimed at bringing the North to the negotiating table and emphasized that Seoul and Washington have no difference in the approach.

The two seem to not to put much emphasis on more than a two-month lull in North Korea's provocations, saying that they have not been able to confirm Pyongyang's real intention.

"I hope that they will stop forever. But we had no communication from them so I don't know whether to interpret it positively or not. We have no signal from them," Yun said.

 Upon arriving in South Korea on Tuesday, Yun said that he did not know why the North had halted its provocations but urged the North to stay provocation-free "for a period of time," adding that it would be a "good start." North Korea has not carried out provocation since Sept. 15, when it fired a missile over Japan.

Asked to clarify his "period of time" observation, he didn't comment.

On Wednesday, China announced that it would send Song Tao, the head of the international department at the Central Committee of the Communist Party of China, as a special envoy to North Korea.

The visit is intended to explain the outcome of its 19th party congress held last month, according to China. It still is drawing much attention, as it comes amid frayed ties between the two neighbors over Pyongyang's defiant pursuit of nuclear weapons.

The foreign ministry later said in a press release that Lee and Yun agreed to meet again "as soon as possible" to discuss detailed follow-up measures based on the talks that they had here.

The ministry added that South Korea's deputy nuclear envoy Jeong Yeon-doo also met on Thursday with his Japanese counterpart on the sidelines of a forum held in Seoul where they discussed ways to make denuclearization efforts for North Korea move forward. (Yonhap)