"Both sides have been engaged in dialogue in regard to a third summit," the President said in an interview shared with Yonhap news agency and six other global news agencies. "It's noteworthy that the behind-the-scenes talks have been preceded by the mutual understanding of each other's position gained through the Hanoi summit," Moon said.
He was referring to the second meeting between US President Donald Trump and North Korean leader Kim Jong-un in February, which ended inconclusive.
According to the South Korean President, conditions are ripe for the resumption of formal denuclearisation talks. "There has already been considerable headway made in the peace process on the Korean Peninsula, and it is still making steady progress," Moon said.
"The resumption of negotiations between North Korea and the US will take it to the next level. I believe everything has now fallen into place for that to happen," he said.
Neither North Korea nor the US have said anything about formal talks since the failed Vietnam summit and Seoul has not been able to explain publicly which communication channels have been maintained with Pyongyang.
Some observers viewed it as thinly veiled pressure on both sides to restart talks immediately, Yonhap reported.
In Hanoi, Pyongyang pushed for a gradual process accompanied by the lifting of US sanctions, while Washington said it would lift sanctions only after Kim dismantled his nuclear programme.
Trump has said he will have talks with Kim "at some point".
Asked by a reporter at the White House whether the summit issue was included in his recent exchange of personal letters with Kim, Trump replied, "Maybe there was, but we, you know, at some point, we'll do that. Getting along very well. He's not doing nuclear testing."
It is also speculated that the US President could visit the inter-Korean border and make a gesture to invite Kim back to the negotiation table.
Talking about Seoul-Pyongyang ties, Moon said the dialogue is going on through "diverse channels" and he is prepared to meet Kim at any time.
The South Korean President is gearing up for a round of brisk bilateral and multilateral summit diplomacy later this week as he will participate in the two-day G20 summit in Osaka, Japan. He will then hold a weekend summit with Trump in Seoul.
Moon is also scheduled to meet Chinese President Xi Jinping on the Osaka session sidelines.
( With inputs from IANS )