During their meeting the two leaders discussed inter-Korean co-prosperity, peace, reconciliation and reunification.
This is only the second ever inter-Korean summit - the first took place in 2000.
Earlier in the day, the South Korean president said he sought common ground with the North Korean leader at the talks.
"We couldn't agree on everything we talked about. We've agreed on some parts and some parts we didn't. But what I can be sure of is we both had a firm intention for establishing peace. We've agreed that there should be a direction in the future for peace."
The two leaders are expected to issue a joint declaration on Thursday morning after the two rounds of talks on Wednesday.
The South Korean president arrived in Pyongyang on Tuesday for a three-day visit.