File Photo: Top leader of the Democratic People's Republic of Korea (DPRK) Kim Jong Un (L) meets with U.S. President Donald Trump in Singapore, on June 12, 2018. (Xinhua/The Straits Times)

WASHINGTON, Sept. 20 (Xinhua) -- The U.S. State Department on Thursday said the denuclearization of Pyongyang has to come first before the U.S. side gives any corresponding reciprocal measures.

When asked about Pyongyang's demand put forward during the just-concluded inter-Korean summit or corresponding measures to dismantle its nuclear complex, U.S. State Department spokesperson Heather Nauert told a press briefing that "Nothing can happen in the absence of denuclearization. Denuclearization has to come first."

During his Sept.18-20 trip to Pyongyang, South Korean President Moon Jae-in held talks with the top leader of the Democratic People's Republic of Korea (DPRK) Kim Jong Un. The inter-Korean summit was the third of its kind this year, following those held on April 27 and May 26.

The top leaders of the two Koreas signed after their talks the Pyongyang Declaration on further steps towards the Korean Peninsula's denuclearization and concrete measures to end hostile acts near inter-Korean border areas.

"Denuclearization is something that has to come," Nauert said at the U.S. State Department press briefing, adding that "any time that we have our government sitting down and talking with their government, that we have President Moon talking with Chairman Kim, it is a step in the right direction; a step in the right direction to start to have regular dialogue."

She said that to allow inspectors from the United States and the International Atomic Energy Agency (IAEA) in the DPRK's nuclear dismantlement, a measure not mentioned in the paper signed during the Pyongyang inter-Korean summit, is part of "a shared understanding."

"Anytime you have a nuclear situation like this where there is a dismantlement ...the expectation is that IAEA inspectors would be a part of that," she added.

"Sanctions must continue to be enforced ... in order to get to the denuclearization," Nauert said.

Moon said Thursday that Kim had expressed his hope to rapidly hold his second summit with U.S. President Donald Trump during the inter-Korean summit in Pyongyang.

Addressing to the people at the Seoul press center for the Pyongyang summit, Moon said he also hoped that the DPRK-U.S. dialogue would be resumed rapidly, noting that conditions were created via the Pyongyang summit to restart the talks between the DPRK and the United States.