Earlier in the day, South and North Korean officials in charge of inter-Korean relations met in Seoul for the first time in nearly two years.
Hyun told reporters that the two sides discussed various inter-Korean issues.
Kim Yang Gon, the visiting North Korean spy chief who also handles issues related to the South, said: "After meeting with several people [in the South] I felt the imperative need for North-South relations to improve."
Meanwhile, a small group of protesters staged an anti-North Korean rally close to the hotel where the North Korean delegation was staying.
The North Korean delegation was scheduled to return home later on Saturday but their departure had been delayed, according to South Korean media.
The delay fuelled speculation that a meeting with President Lee would possibly occur.
The North Koreans had come to Seoul to pay tribute to the late Kim Dae-Jung, a former South Korean president who died last week.
Kim was cherished on both sides of the border for his pursuit of closer ties between the two states.
His "sunshine policy" engagement and aid to the impoverished North earned him the Nobel Peace Prize in 2000 and he held a landmark summit with Kim Jong-il, the North Korean leader, the same year.
The last time officials responsible for inter-Korean affairs met was in late 2007 under the administration of Roh Moo-hyun, the former South Korean president.
Cross-border tensions have risen sharply in recent months after the North made threatening gestures to the South, fired a series of missiles and staged a second nuclear test which resulted in tougher United Nations sanctions.