Tensions on the Korean Peninsula plummeted to their lowest level in years in 2010 following the North's deadly sinking of a South Korean warship and the bombardment of a southern island.
Military talks intended to ease tensions between the two Koreas broke down last month after the North's representatives refused to accept the South's demand that Pyongyang apologize and take responsible measures for its attacks.
"A heartfelt apology (by North Korea) over the two provocations last year could become a starting point to opening new South-North relations," Kim Tae-hyo, President Lee's deputy national security adviser, told a security forum in Seoul.
North Korea's apology for the attacks and its promise not to repeat such provocations are among the three key conditions that Seoul says Pyongyang must fulfill before the two sides can improve relations. A third demand has been that the North demonstrate its denuclearization commitment through action.
Despite high tensions, Kim said his government is planning to offer humanitarian aid to help children and underprivileged people in North Korea.
"From the humanitarian point of view, the government is pushing for aid for children and the vulnerable in North Korea," Kim said, describing the push as "smart aid."
Tensions on the Korean Peninsula remain high after the Cheonan warship sank last March from a North Korean torpedo attack, killing 46 sailors. In November, the North shelled a South Korean border island in the Yellow Sea, killing four people, including two civilians.