Lee earlier on Monday expressed regret over at least two incidents of drone incursions across the border that he said had been carried out by South Korean individuals violating government policy, calling it an act of "revolt" against their own country.
North Korea has said that drones sent from south of the border had violated its airspace, accusing South Korea of a serious provocation and saying it had shot them down.
"Our government appreciated it as a very fortunate and wise behaviour for its own sake," Kim Yo-jong, North Korean leader Kim Jong-un's influential sister, said in a statement carried by KCNA state news agency, referring to Lee's remarks.
Kim Jong-un considered it "a manifestation of a frank and broad-minded man's attitude," she said.
Kim Yo-jong often makes comments on North Korea's external policy matters believed to reflect her brother's views.
The comments were in stark contrast to the scathing attacks by North Korea in recent years against what it called its "most hostile enemy" with which it could no longer pursue a goal of eventual unification.
The two Koreas remain technically in a state of war after their 1950-53 armed conflict ended in a truce.
Lee said an investigation has concluded a National Intelligence Service (NIS) employee and an active-duty military official were involved in the drone incidents, adding they violated South Korea's constitution that forbids acts of provocation against North Korea.
"Although it was not our government's intention, we express our regret to the North over the fact that unnecessary military tensions were caused by the irresponsible and reckless actions of some individuals," Lee said in a cabinet meeting.
Lee has made several overtures to the North since taking office in June to improve ties, which had plunged to among the worst in decades, saying peace was the best policy for both sides to achieve prosperity.
