In written answers to questions submitted by leading media, Moon -- who brokered talks between US President Donald Trump and North Korean leader Kim Jong Un last year -- also urged Pyongyang to resume the dialogue to show its desire to denuclearise.
Moon is set to host the US leader this weekend as he tries to rekindle nuclear talks that have stalled since the collapse of a second summit between Trump and Kim in Hanoi in February.
The pair failed to reach an agreement on sanctions relief and what the North might be willing to give up in return, and Pyongyang has since not responded to calls for dialogue, maintaining only minimal contact.
"There is no reason to regard the current situation as a stalemate in the peace process on the peninsula just because the pace has remained slow," Moon said.
Trump and Kim's willingness to engage in dialogue had "never faded", he added in the interview with editors of major news agencies including AFP, noting a recent exchange of letters between them.
On Sunday, the North's state media reported that Kim received a personal message "of excellent content" from the US president, just days after Trump said the North Korean leader had sent him a "beautiful letter".
Trump has insisted he was in "no rush" for a third meeting with Kim, but Moon said Wednesday that "behind-the-scenes talks" were going on between Pyongyang and Washington for another summit.
Despite the top-tier correspondence, US officials say privately the North has been sitting on their offer for working-level talks and the South Korean unification minister recently admitted that the talks process was at a standstill.
Moon said the implementation of agreements between the US and North Korea requires patience, given their long history of hostility.
"As their hostile relations have persisted for more than 70 years, it will be difficult to cross a sea of mistrust all at once," he added.
The two have blamed each other for the collapse of the Hanoi summit, with the US saying Pyongyang sought the lifting of effectively all major sanctions for partial disarmament, while the North says it wanted some measures eased for closing all the nuclear facilities at its Yongbyon complex.
North Korea has since accused the US of acting in "bad faith" and last month raised tensions by launching short-range missiles for the first time since November 2017.
But Moon insisted that the resumption of missile tests did not trigger a "sudden hike in tensions" nor lead to "a breakdown of the denuclearisation dialogue".
On the question of the North's commitment towards a full dismantlement of its nuclear programme, Moon called on Pyongyang to return to the dialogue table "at the earliest date possible".
"If Pyongyang leaves behind the passive stance it has adopted following the summit in Hanoi... this will help it win the trust of the international community," he added.
At the same time, Moon said, "North Korea must trust the promise of the international community to ensure its security and a bright future."
In written answers to questions submitted by leading media, Moon also urged Pyongyang to resume the dialogue to show its desire to denuclearise.