In this regard, they reaffirmed their willingness to "transform their respective relationships with North Korea, end nearly 70 years of hostility and establish a permanent peace regime on the Korean Peninsula," it added in an English-language statement.

While this wording did not appear in the US readout, the official said, the wording was coordinated between the allies' National Security Councils.

Speaking on condition of anonymity, he noted that the US has agreed to use the word "transform," which was unthinkable when John Bolton, known for his hawkish view on Pyongyang, served as Trump's national security adviser.

Some other American officials, including Secretary of State Mike Pompeo and Special Representative Stephen Biegun, have talked publicly about "transforming" the Washington-Pyongyang relationship.

The Seoul official, however, stressed that it was "the very first time (for the word) to be used between the two houses -- White House and Blue House -- which showcases how willing and resolved the two top leaders are committed to transforming the relationship with the DPRK," according to an audio file released by Cheong Wa Dae. DPRK is the initialism for the North's official name, the Democratic People's Republic of Korea.

Hopefully, he added, Pyongyang will accept it as "a very strong, or reassuring signal" that Seoul and Washington are "ready to transform the relationships to a level that we've never been to, in other words, terminating 70 years of hostility."

He was responding to the view of some local media that Cheong Wa Dae may be attaching excessive meaning to it in an apparent bid to publicize the summit results.

In fact, Trump stated in his Singapore summit accord with North Korean leader Kim Jong-un last year that the two sides "commit to establish new US-DPRK relations in accordance with the desire of the peoples of the two countries for peace and prosperity."

It's uncertain whether the US draws a clear distinction between "transforming" ties with Pyongyang and "establishing" new ones.

The Seoul official also took note of the reappearance of Kim Kye-gwan, a veteran North Korea nuclear negotiator, with a special message carried by Pyongyang's state news agency on Thursday.

"I came to know that President Trump is different from his predecessors in a political sense and decision (making) while watching his approach to the DPRK, so I would like to place my hope on President Trump's wise choices and bold decisions," Kim, who now works as an adviser to the North Korean foreign ministry, said.

Kim was emphasizing that the US should bring a new set of methods for negotiations, decided by Trump himself, the South Korean official said.

He added it was quite interesting that Kim has mentioned two things -- the South Korea-US combined military exercises and sanctions -- which represents a clear signal from Pyongyang.

On ways to move forward the denuclearization process, the official said dismantling the Yongbyon nuclear complex could be an "irreversible" starting point, as the North has already committed to giving it up.

"Once you have confidence in irreversible denuclearization, whether you like (it) or not, it has to be incremental," he said.

Another fruit of the latest Moon-Trump summit was a confirmation that there's "no daylight" between the two sides, he said. After the New York session, the White House stated the two sides agreed that their alliance remains the "linchpin" of peace and security on the Korean Peninsula and in the region.

Moon would like to have another summit with Trump before the end of this year, the official added.

Regarding Moon's suggestion during his keynote speech at the U.N. General Assembly of turning the Demilitarized Zone (DMZ) into an international peace zone, the official said it was a message to Pyongyang, presented as a kind of "security guarantee."

Transforming the DMZ into a U.N.-backed peace zone would be conducive to preventing another war on the peninsula, he said, as the Moon administration is striving to help clear obstacles to the denuclearization process so that Pyongyang and Washington can concentrate on "big talks."

"That will be our role (for now). And obviously when (the talks) become so productive ... they get to the point (where) they talk about a peace regime on the Korean Peninsula, we will intervene. We'll be a big part of it," he said.

He also stated that the two Koreas are continuing "regular contacts and communications" via their liaison office in the Kaesong industrial complex and the eastern military hotlines in Goseong, Gangwon Province, which function like the embassies of two "normal states."

Asked about the prospects of Seoul-Washington bargaining on sharing defense costs, the official said his government wants to share the burden in a "rational" way to reflect the "reciprocal dynamics" of the alliance, how much South Korean taxpayers are willing to accommodate and Seoul's efforts to beef up its own defense capabilities.

He said the Moon administration does not intend to use the purchase of US weapons as leverage in the Special Measures Agreement talks on deciding the level of Seoul's financial contribution to the presence of US Forces Korea.

Acquiring more US military assets is part of preparing for the transfer of wartime operational control, he said.

In Moon's latest hourlong talks with Trump, meanwhile, issues related to Japan or an OPCON transition schedule were not discussed, he said. (Yonhap)