Nauert did not respond when asked if the United States was willing to take "corresponding measures", except to say: "Nothing can happen in the absence of denuclearization; denuclearization has to come first".
It also was unclear what "corresponding steps" North Korea wants from the U.S.to dismantle its nuclear site.
"I have a dream that I have not been able to fulfil for a long time, which is trekking Mount Paektu and the Kaema Plateau (in North Korea)", Mr Moon said during a banquet after his first summit with Kim in April, which took place at the demilitarised zone separating the two neighbours.
North Korean leader Kim Jong-un and South Korean president Moon Jae-in started it off by hugging in Pyongyang Sunan International Airport.
The summit communique had a weaker and more conditional denuclearization pledge than that which North Korea had agreed to 13 years to the day earlier when it "committed to abandoning all nuclear weapons and existing nuclear programs and returning, at an early date, to the Treaty on the Non-Proliferation of Nuclear Weapons and to IAEA Safeguards" in the September 2005 Six Party Talks Joint Statement.
"There were hopes the inter-Korean summit would break the current stalemate between Pyeongyang and Washington in their denuclearization talks".
But while containing several tantalizing offers, their joint statement appeared to fall short of the major steps many in Washington have been looking for - such as a commitment by Kim to provide a list of North Korea's nuclear facilities, a solid step-by-step timeline for closing them down, or an agreement to allow worldwide inspectors to assess progress or discover violations.
"We have agreed to make the Korean Peninsula a land of peace that is free from nuclear weapons and nuclear threat", Kim said. That prompted Pompeo to invite North Korean Foreign Minister Ri Yong Ho to meet in NY next week, where both are scheduled to attend the United Nations General Assembly.
U.S. Secretary of State Mike Pompeo said on Wednesday he had invited North Korea's foreign minister to meet in NY next week and other Pyongyang officials to Vienna for talks with nuclear envoy Stephen Biegun.
"I think it's beneficial that [denuclearization] was raised as a topic", Paal said. He added, "Without disarming nuclear weapons and their fuel ... and destroying ballistic missiles ... we have a long way to go".
"The Chinese envy us because they can't go down to the lake from their side but we can", Kim said. Moon also appeared to be making good on his proposals to help build up the North's infrastructure and open cross-border rail links.
The announcement came as surprise to South Koreans, who have never seen the North Korean leaders crossing into the South Korean territory after the 1950-53 Korean War divided the Korean Peninsula.
Pyongyang is also likely to reiterate its demand for the withdrawal of US troops from the peninsula, Paal said. And South Korea's director of national security, Chung Eui-yong, has said that North Korea will not ask for the removal of USA units in South Korea. Seoul increasingly sees denuclearization as a U.S.
Bruce Klingner, a onetime intelligence officer specializing in Korean affairs who is a senior research fellow at the Heritage Foundation, said evidence points to the contrary. "They don't meaningfully constrain North Korea's nuclear programme".
FILE - South Korean Army K1A1 and U.S. Army M1A2 tanks fire live rounds during a U.S. "We have lived together for 5,000 years and lived in separation for 70 years".
"This is what an Israel-style deal looks like with North Korea: They pretend to disarm and we pretend to believe it".
"We are not going to fall into that trap", Keane said.
But there have been concerns in South Korea and the United States that ending the war would ultimately prompt China and Russian Federation, if not North Korea, to demand that the United Nations Command (UNC), which overlaps with US forces in South Korea, be disbanded and leave.
After the two leaders pledged new steps aimed at salvaging nuclear talks on Wednesday, Moon and Kim made a decision to use the final day of their three-day summit to go up the symbolic mountain on the Chinese border together. "Many, particularly in Seoul, are advocating relief or release from sanctions".
The new Pyongyang Declaration is a really big deal to South Korea and North Korea. Indeed, much of the Declaration has been covered in previous inter-Korean agreements.
Removal of 11 guard posts in the demilitarized zone by the end of the year. "So that would just be normal course of doing business".