Abe and Trump spoke for about 20 minutes and tentatively set a date of November 17 for the meeting, just before Abe goes to Peru for the Asia-Pacific Economic Cooperation (APEC) summit, a Japanese foreign ministry official told AFP.
During his election campaign, Trump raised eyebrows in Japan by calling on the country to pay more to support the cost of stationing US forces.
He even suggested that Japan might want to become a nuclear power to counter unpredictable neighbour North Korea, which has repeatedly conducted nuclear and ballistic missile tests to international condemnations and prompting UN sanctions.
That statement shocked many in Japan, the only country in the world to have been attacked with nuclear weapons.
Trump has also rejected the Trans-Pacific Partnership free trade deal pushed by President Barack Obama and which Abe hopes his parliament will ratify soon.
Abe congratulated Trump soon after his victory on Wednesday, vowing that the countries would maintain their close relationship, calling them “unshakeable allies”.
During their phone talks, Abe “talked about the importance of the bilateral relationship and the Japan-US alliance”, which he stressed underpins the peace and stability of the Asia-Pacific region, the foreign ministry official said.
In response, Trump said he hoped to strengthen the US-Japan relationship further, the official said.
Trump also said he appreciated Abe’s economic policy and looked forward to working with him, she said.
She declined to elaborate on what else they discussed.