Abe's conservative coalition secured a landslide win, winning more than 300 seats in the 465-seat parliament in snap polls yesterday.
Trump is scheduled to visit Japan early next month.
The president "spoke yesterday with" Abe to congratulate him on his recent electoral victory, the White House said.
"The two leaders underscored the importance of a free and open Indo-Pacific region, and a strong United States-Japan alliance," it said.
During the telephonic conversation, Trump reaffirmed his desire to continue working closely with Abe, and said he looks forward to visiting Japan in early November.
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"The president will commence this visit to Asia beginning with Japan on November 5," a senior Trump administration official told reporters at the White House in a preview of the visit from November 3 to 14.
"In Japan, he is going to affirm the US-Japan Alliance as the cornerstone for regional peace and security. The president's meetings in Japan will focus on ways for the US and Japan to work together to promote a free and open Indo- Pacific Region," the official said.
Responding to questions on media reports, the official said that it would not be surprising that the two leaders play golf during the trip.
Trump and Abe, the official said, have forged a personal relationship that they have built upon in terms of "our alliance, our close economic ties, cultural ties and the values that the United States and Japan share".
On the other hand, Trump has a very good working relationship with Chinese President Xi Jinping.
Trump wants to continue building on what the president terms a constructive and result-oriented relationship with Xi.