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North Korea's leader has called for a "further livening up" of the "warm climate of reconciliation" with the South created by the Winter Olympics.
Kim Jong-un, whose nuclear bomb and missile tests have stoked international tension, praised the South for hosting his state at the games in Pyeongchang.
Kim's apparent Games charm offensive was led by his sister Kim Yo-jong.
South Korean President President Moon Jae-in has meanwhile said the US is open to talking with the North.
He did not elaborate and may have been referring to a remark by US Vice-President Mike Pence on his flight back to Washington from the Games.
"If you want to talk, we'll talk," Mr Pence was quoted as saying by the Washington Post.
While the North's attendance at the Games has been seen as marking a major warming in relations, there have also been concerns that it has allowed it to win a propaganda victory.
He thanked the South for "specially prioritising" the North's attendance at the Games, North Korean state news agency KCNA reports.
Ms Kim's visit has been one of the most talked-about aspects of the Games
He also gave "important instructions" on how to "liven up" the "warm climate of reconciliation and dialogue".
A picture released by the agency shows Mr Kim flanked by his sister and the North's ceremonial head of state, Kim Yong-nam, both linking arms with him.
Ms Kim and Mr Kim Yong-nam made up the most senior delegation from the North to visit the South since the Korean War in the 1950s.
The two states have never signed a peace treaty and are in a constant state of mutual distrust.
On Saturday, Ms Kim handed over a letter from her brother to President Moon, inviting him to visit Pyongyang. If the summit goes ahead, it will be the first meeting in more than a decade between Korean leaders.
Ms Kim's appearance at the Games has been widely criticised, as she is on a US sanctions list over alleged links to human rights abuses in North Korea.
She headed the North's delegation and has now returned home.
By Laura Bicker, BBC News, Pyeongchang, South Korea
You could almost feel the ripple of excitement as Kim Yo-jong walked into the opening ceremony of the Winter Olympic Games. Necks craned and mobile phones were held aloft to catch a glimpse.
I found myself, along with others, leaning as far as I could over the balcony to try to see her in the VIP box below. The faces around the stadium all said one thing: she's here, on South Korean soil.
She has given the secretive regime a human face.
Her country is subject to a raft of sanctions from the US, the UN and the EU over its weapons programmes and Japan has said it remains sceptical about the "charm offensive".
"I am aware that some people argue that because North Korea is engaging in dialogue we should reward them," Foreign Minister Taro Kono said before the Games.
"Frankly I think this view is too naive. I believe that North Korea wants to buy some time to continue their nuclear missile programme."
Mr Pence stressed the US would continue imposing sanctions and putting pressure on Pyongyang.
North Korea's presence at the Games raised concerns about a propaganda victory
"The point is, no pressure comes off until they are actually doing something that the alliance believes represents a meaningful step toward denuclearization," Mr Pence told the Post.
"So the maximum pressure campaign is going to continue and intensify."
Mr Pence came face to face with Ms Kim at the opening ceremony of the Winter Olympics, but they did not interact.
Kim Yo-jong was seated in the row behind US Vice-President Mike Pence at the opening ceremony
