The South's Unification Ministry confirmed the meeting in the border truce village of Panmunjom had ended after two relatively short sessions, but gave no immediate details of the outcome.
A first round was held at Panmunjom on Wednesday and marked the highest level North-South talks for seven years.
South Korea wanted the North to guarantee that a planned reunion for relatives divided by the 1950-53 Korean War would take place as scheduled at the North's Mount Kumgang resort from February 20-25.
The talks were the first substantive follow-up to statements by the leaders of both countries - South Korean President Park Geun-Hye and the North's Kim Jong-Un - professing a desire for improved inter-Korean ties.
An eventual compromise on the overlapping family reunions and military drills could signal a willingness to explore other, far more contentious issues, according to Robert Carlin, a former US State Department official and contributor to the closely-followed North Korea-dedicated website, 38 North.
There had already been signs of a shift in position at Wednesday's first round, with the North's demand that the annual South Korea-US exercises be postponed.
North Korea routinely condemns the drills as provocative rehearsals for war, and its previous position has always been to demand their permanent cancellation.
By calling for this year's exercises to be delayed, Pyongyang seemed to indicate that it could live with them actually going ahead - if Seoul and Washington conceded on the scheduling.
Seoul's initial response has been an unequivocal rejection of any change to the military drills, on the principle that there can be no linkage between them and an essentially humanitarian issue like the family reunions.
That position was echoed yesterday by visiting US Secretary of State John Kerry, who urged Pyongyang to act with "human decency" and not try to use "one (issue) as an excuse to somehow condition the other".
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