Nauert said behind-the-scenes discussions with Pyongyang have normalized in the wake of President Donald Trump's June summit with North Korean leader Kim Jong-un and subsequent meetings between US Secretary of State Mike Pompeo and other top Pyongyang officials.
With that in mind, Moon said only when "complete denuclearization" and "peace" are established on the Korean Peninsula, "economic cooperation can be carried in earnest".
In a message to Kim on the North's National Liberation Day - marking the end of Japanese rule over Korea at the end of World War II - Putin reiterated his intention for a summit.
He also expressed concern to not get sidetracked by other players in the security of the peninsula.
President Moon Jae-in on Wednesday proposed using railroads to bring together the two Koreas, Japan, China, Russia, and Mongolia and having the United States as a project partner in an address commemorating the 73rd Liberation Day.
"The development of South-North Korean relations is not an additional outcome of development in North Korea-US ties".
At their next summit in September in Pyongyang, the two leaders will "take an audacious step to proceed toward the declaration of an end to the Korean War and the signing of a peace treaty, as well as the complete denuclearisation of the Korean Peninsula", Moon added.
Moon added that the re-establishment of those connections would lead to the creation of an "East Asian Railroad Community" that encompasses six Northeast Asian countries and the United States. "Rather, the development of South-North Korean relations is the driving force that promotes denuclearisation of the Korean Peninsula", Moon said.
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North Korea wants economic concessions after each step of the denuclearization process.
The North has urged the United States to end the sanctions, saying it had made goodwill gestures, including a moratorium on nuclear and missile tests, the dismantling of a nuclear site, and the return of the remains of some USA soldiers killed in the Korean War.
Moon held out the promise that restored economic ties could generate $149 billion for North Korea over 30 years.
Last month, the North's state media criticized the South accusing it of only caring only about the views of the United States and failing to take practical steps to advance inter-Korean relations.
The United States opposes lifting any sanctions until the North completely denuclearizes.
However, Moon also said economic cooperation with North Korea is linked to that country's denuclearization. Meanwhile the USA has urged the worldwide community to maintain tough sanctions on the isolated regime-Seoul has caught three South Korean firms importing coal and iron from the North past year in violation of the measures.