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 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.
How big a propaganda coup has the North scored?
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.
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