Moon, who was invited a day after the opening ceremonies to Pyongyang for a summit with Kim Jong Un, also said that Washington and Pyongyang should quickly meet to "fundamentally solve" the standoff on the Korean Peninsula.
The U.S. president's daughter and adviser said Sunday that her visit to the Olympics was "so incredibly inspiring" and expressed gratitude at the chance to watch competition and - in a subtle nod to Korean Peninsula politics - "be here with our allies in South Korea".
Moon's office did not reveal, for example, whether North Korea had attached any preconditions for starting talks with the United States like the suspension of joint South Korea-US military exercises, which it calls a rehearsal for invasion.
Mr Watters told Fox News: "I like how the Trump administration has slowly delivered stronger and stronger sanctions without letting North Korea know that there's a phase two, maybe there's a phase three". Ivanka Trump has some popularity in Asia, and the perception of her as a smoother player in her father's administration - and, not inconsequentially, a younger one as well - allows the United States a photogenic representative at a games dominated by unusually adept PR moves from North Korea.
This article has been adapted from its original source.
As she arrived with the U.S. delegation in South Korea Saturday, White House Press Secretary Sarah Sanders had said no talks were scheduled.
"Ivanka Trump has been briefed on this".
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The visit by Kim Yong Chol, heading an eight-member delegation that crossed the Demilitarized Zone Sunday morning, is the final piece of the Games-led diplomacy that has dominated headlines from Pyeongchang after months of tensions. "Presidential delegation's attendance at the closing ceremonies was the culmination of a successful trip where we celebrated the Olympic Games, U.S. athletes and our strong alliance with South Korea".
There was no immediate comment from the United States, where it was dawn when the statement was released.
In response, the White House later on Sunday said that it "will see" if North Korea's willingness to hold talks represents a commitment to abandon its nuclear weapons programme.
At a White House news conference on Friday, he warned that the US would move to "phase two" in its pressure campaign if sanctions don't work.
Jesse Watters, a conservative commentator for Fox News, said this slow, incremental rise in pressure, without revealing the next steps, would only drive Kim Jong-un's paranoia.
The revelation from the South Korean presidency came hours after a furious statement from the North that described fresh sanctions announced by Washington as "an act of war".
She also delivered an invitation from her brother for Moon to visit North Korea.
"Like we have said repeatedly, we would consider any restrictions on us as an act of war, and we will not stop the USA if it really has the guts to confront us in a "rough" manner", the state-run KCNA news agency quoted the North's Foreign Ministry statement as saying.