The message from the South Korean leader to the US came even as the two allies pursue increasingly different approaches towards Pyongyang.
Washington has shied away from a formal announcement that the 1950-1953 conflict, which ended with an armistice rather than a peace treaty, has ended, saying that North Korea must first take more steps towards giving up its nuclear arsenal.
For its part, Pyongyang – which long insisted it needed nuclear weapons to defend itself against a possible US invasion – has pledged only to work towards denuclearisation “of the Korean Peninsula”, demanding simultaneous moves by Washington in return, with a peace declaration its first priority.
“The North has stopped all nuclear and missile tests, dismantled its only nuclear test site and is now dismantling its missile engine test facilities and is promising to take steps toward dismantling its Yongbyon nuclear complex, if the US takes corresponding measures,” Moon told the BBC.
“Declaring the end of the war is a political declaration that the US would end decades of hostile relations with the North,” he said.
“Moving towards such a process is the corresponding measure the US should take,” he added.
The comments, made ahead of Moon’s departure on Saturday for a tour of European capitals, highlight the increasing differences between Seoul and Washington, which has 28,500 troops stationed in the South to defend it from its neighbour.
Experts say the offers made by North Korea will have little impact on its military capabilities, and Pyongyang itself has said it has no further need to test its weapons.
Moon has long favoured engagement with the North, which is subject to multiple UN Security Council sanctions over its nuclear and ballistic missile programmes, and visited Pyongyang last month for his third meeting with leader Kim Jong Un.
Moon has dangled large investments and joint cross-border projects as incentives for steps towards denuclearisation, with Seoul opening a joint liaison office in the North Korean border city of Kaesong last month and promising to pursue cross-border road and rail projects.
The US, which spearheaded global efforts to squeeze the North Korean economy last year, has been adamant that the sanctions remain in place until Pyongyang’s “final, fully verified denuclearisation”.
But after a visit by US Secretary of State Mike Pompeo to Pyongyang, Trump said this week that a second summit between him and North Korean leader Kim Jong Un could happen after the US midterm elections in early November.
Kim and Trump traded personal insults and threats of war last year before a rapid rapprochement culminated in their historic first meeting in Singapore in June.
Critics, however, said their joint statement saw Kim make only a vague commitment towards denuclearisation, with no concrete measures.
Seoul said separately that the two Koreas will hold high-level talks at the border on Monday to discuss how to implement the agreements made at last month’s Pyongyang summit.