Relations between North and South Korea nosedived during 2010 South Korea has agreed to high-level military talks with the North, after months of tension on the peninsula.
The South said it would join the talks only if the agenda included the two events that have soured relations - the sinking of a southern warship in March, and the shelling of a southern island.
Pyongyang denies torpedoing the Cheonan warship, and says it was provoked into shelling Yeonpyeong island in November.
On Wednesday, the US and China urged the two sides to reopen talks.
The North had made several offers of talks earlier this month, but they were all dismissed by Seoul.
Officials at the South's defence ministry said the North made its latest offer of talks in a telegram sent to southern Defence Minister Kim Kwan-jin, signed by the North's Armed Forces Minister Kim Young-chun.
The South's Unification Ministry said the offer included a commitment to "exchange views" about the shelling of Yeonpyeong and the sinking of the Cheonan.
The ministry said the offer had been accepted, but that the North must give assurances that it would "take responsible measures" over the two incidents.
'Fence-mending'On Wednesday, China's President Hu Jintao and US President Barack Obama released a joint statement urging Korean dialogue after a meeting in Washington.
Analysis
South Korea has rejected previous calls from the North for talks. So what has changed?
It is suggested that the North has finally agreed to "exchange views" with the South on the sunken warship and the island which was bombarded. That falls short of the apology demanded by Seoul, though it is movement.
In the coming weeks, preparatory talks are expected about discussions between more senior figures, whether military or ministerial. Seoul may walk away if it feels that Pyongyang is still "insincere".
There is likely to be significance in the timing of this latest move, with the American and Chinese presidents recently calling for measures that would allow the early resumption of multilateral talks on North Korea's denuclearisation.
"The United States and China emphasised the importance of an improvement in North-South relations, and agreed that sincere and constructive inter-Korean dialogue is an essential step," the two leaders said.
And the North's state-run news agency KCNA called for the US to reopen talks with Pyongyang.
"The US would be well advised to re-examine its hostile policy towards the DPRK [North Korea] and make a U-turn towards dialogue and fence-mending," its report said.
The US is among the countries involved in talks over the North's nuclear programme.
Pyongyang pulled out of the talks in April 2009, shortly before conducting a nuclear test.
Southern defence officials said on Thursday that they would propose to Pyongyang reopening dialogue on denuclearisation.
Relations between the two Koreas plunged to new lows after the South's Cheonan warship was sunk in March, with the loss of 46 lives.
An international report later blamed the North for the sinking - allegations denied by Pyongyang.
On 23 November, the North killed four people when it shelled Yeonpyeong island - its first attack on a civilian area since the 1950-53 war ended.
The South responded with a series of military exercises close to the border.
