Spokesman Kim Eui-kyeom said President Moon Jae-in had a phone call with Abe Sunday, during which the two leaders agreed to create an environment that can lead to a successful denuclearization pact between the United States and North Korea.
Abe is said to have "highly assessed" the Korean agreement to pursue a full denuclearization of the Korean Peninsula, through the Panmunjom Declaration made Friday after Moon and Kim Jong Un's historic summit.
During his meeting with Kim, Moon is known to have brought up the issue of Japanese nationals detained in North Korea, Chosun Ilbo reported.
The South Korean president promised to act as a bridge between Pyongyang and Tokyo, telling the Japanese PM Kim is willing to speak with him and normalize ties with Japan.
Moon also spoke to Russian President Vladmir Putin, and the Russian leader said there's a need to ensure the achievements of the inter-Korean summit lead to joint cooperation between the two Koreas and Moscow, Yonhap reported.
He said Moscow's railway, gas and power systems could be connected to the Korean Peninsula through Siberia, adding to the stability and prosperity of both Koreas.
Putin also requested Moon's visit to Russia before the World Cup opens in June.
Next month, Moon is set to hold back-to-back summits with the United States, China, Japan and Russia.
The South Korean president is expected to hold a phone conversation with Chinese leader Xi Jinping in a few days, due to Xi's domestic engagements.