Abe talked briefly with recently elected South Korean President Park Geun Hye, though neither nation's foreign ministry opted to disclose the topics discussed.
Abe held a bilateral meeting with Chinese President Xi Jinping Thursday, at which the two leaders briefly talked about the disputed islands in the waters separating their two countries, The Yomiuri Shimbun reported.
China's official Xinhua news agency said Xi told Abe the conflict over the islands is "exactly what I don't want to see."
"Japan should face history squarely and deal appropriately with such sensitive issues as the Diaoyu Islands [the Chinese name for the Senkakus] and historical matters from a future-oriented standpoint so as to resolve the problems by getting differences in bilateral standpoints under sufficient control," Xinhua quoted Xi as saying.
In response, Abe said the two countries "should return to the starting point of their mutually beneficial strategic relationship to ensure ties between Japan and China progress."