SEOUL, South Korea >> A rare invitation to Pyongyang for South Korea’s president marked Day Two of the North Korean Kim dynasty’s southern road tour, part of an accelerating diplomatic thaw that included some Korean liquor over lunch and the shared joy of watching a “unified” Korea team play hockey at the Olympics.

Nothing has been settled on any trip north by South Korean President Moon Jae-in. But the verbal message today to come at a “convenient time” from dictator Kim Jong Un, delivered by his visiting younger sister, Kim Yo Jong, is part of a sudden rush of improving feelings between the rivals during the Pyeongchang Olympics. The result: a heady, sometimes surreal, state of affairs in a South Korea that has seen far more threat than charm out of the North.

Still, it wouldn’t be South Korea if people weren’t asking the perennial question when it comes to North Korea changing gears and showering its rival with apparent affection: What’s in it for Pyongyang?

Past “charm offensives” have been interpreted as North Korea trying to recoup from crippling sanctions on their nuclear program, or trying to drive a wedge between Seoul and its U.S. ally.

A massive military parade in Pyongyang on the eve of the just-opened Pyeongchang Games has been used as Exhibit A by skeptics. In it, Kim Jong Un highlighted several huge intercontinental ballistic missiles, which were successfully flight tested three times last year and could reach deep into the U.S. mainland when perfected.

Even so, there’s also cautious optimism, or curiosity at least. If peace isn’t imminent, a summit in Pyongyang between Moon and Kim Jong Un seems preferable to recent months’ threats.

Moon told Kim Yo Jong that the North and South should continue to build conditions for a summit, Moon spokesman Kim Eui-kyeom said. The U.S. and the North should quickly resume dialogue, he said.

Kim Yo Jong was to have lunch Sunday with South Korean Prime Minister Lee Nak-yon, the country’s No. 2 official, and return to Pyongyang on Kim Jong Un’s private jet later in the day.

The lunch Saturday at Seoul’s presidential mansion between Moon and Kim Yo Jong was the most significant diplomatic encounter between the rivals in years. The night before, Kim and other North Korean delegates attended the opening ceremony of the Olympics, watching a “unified” Korean team march under a banner showing an undivided Korean Peninsula.

In a surreal mixture of dignitaries, the Olympic Stadium’s VIP box included Kim Yo Jong and North Korea’s nominal head of state, Kim Yong Nam, sitting above and behind U.S. Vice President Mike Pence and fellow hard-liner Shinzo Abe, Japan’s prime minister. Pence and the Kims seemed to go out of their way not to acknowledge each other.

That was not the case with Moon — either at the games, when he enthusiastically reached up to shake Kim Yo Jong’s hand, or at the lunch the next day. South Korean television showed its smiling president entering a reception room Saturday and shaking hands with the North Koreans.

The opening part of the talks was mostly about the weather: Pyeongchang was colder than Seoul, it was agreed.

“You went through a lot of trouble braving the cold until late” last night, Moon told the North Koreans, referring to their attendance at the frigid opening ceremonies.

At the luncheon proposed a toast, calling for peace and “mutual prosperity” for the two Koreas. He then recalled his past visit to the North’s Diamond Mountain resort, where he and his mother met his North Korean aunt during a temporary reunion of families separated by the 1950-53 Korean War.

He also talked about visiting the North Korean border town of Kaesong, where the countries operated a jointly-run factory park that had been a symbol of rapprochement before South Korea shut it down in 2016, after North Korea’s fourth nuclear test.

“But I haven’t been to Pyongyang,” Moon said, according to comments provided by his office.

Kim Yo Jong said she hopes to see Moon in Pyongyang soon so that he and her brother could “exchange views over many issues,” which she said would make “North-South relations develop like yesterday was a long time ago.”

“We hope that President (Moon) could leave a legacy that would last over generations by leading the way in opening a new era of unification,” she said.

After sitting at a table, Kim Yo Jong placed a blue document folder in front of her. She later gave that folder to Moon, and Moon’s office said it was a personal letter from her brother. Officials didn’t reveal what was written in it.

After meeting with Moon, the North Korean delegates boarded a bullet train to Gangneung, a coastal city hosting some Olympic events. Later Saturday night, they all joined the chief of the International Olympic Committee to watch the debut of the inter-Korean team in the women’s ice hockey tournament. The Koreans were crushed by Switzerland, 8-0.

Pence’s office didn’t directly address Kim’s invitation to Moon. “The vice president is grateful that President Moon reaffirmed his strong commitment to the global maximum pressure campaign and for his support for continued sanctions,” Pence spokeswoman Alyssa Farah said when asked about the developments.

But Pence said that Moon told him “a bit” about his meeting with the North Koreans, and that he “appreciated him sharing his perspective on that.”

“I leave here very confident that we are going to continue to do the things we’ve known have to be done to continue to pressure North Korea to abandon their nuclear ambitions,” Pence said.

Moon is eager to use Kim Yo Jong’s presence at the games to restore regular communication with North Korea and eventually pull it into nuclear talks. Many in Seoul, however, while interested in the warming high-level contacts, are also tempering expectations for a real breakthrough.

There’s worry, too, that the proposed summit in Pyongyang may come with preconditions — a North Korean specialty. A big one could be a demand to cease the U.S.-South Korean war games that North Korea claims are preparation for invasion.

But Moon, a liberal who has always wanted to engage the North, will also have to convince a good portion of his own people who are deeply wary about North Korean intentions.

Among the reasons for skepticism: The accusations that South Korea has had to arrange huge payouts for past meetings, and that these earlier encounters, while producing indelible images, have done little to slow North Korea’s pursuit of nuclear weapons.

Even if there are more meetings between the rivals after the Games, accomplishing something is another matter. South Korea wants a northern neighbor without nukes; North Korea vows to keep its weapons until the United States discards its “hostile” policies against the country.

Hours before Friday’s opening ceremony in Pyeongchang, Japan’s Abe warned Moon not to fall for North Korea’s “smile diplomacy” during the Olympics, according to Moon’s office. Pence carried a similar message.

They seem to have gone unheeded.

“Kim Jong Un is clearly serious about reviving talks with the South to improve relations,” said Koh Yu-hwan, a North Korea expert at Seoul’s Dongguk University and a security adviser to Moon.

“It seems clear,” he said, “that the countries have entered a phase of restoring a regular level of contact.”