By Agence France-Presse
The conversation comes just days after Trump formally withdrew the United States from the Trans-Pacific Partnership, a vast trade deal encompassing a dozen nations that Abe has backed enthusiastically.
US participation is seen as key to the agreement and Abe said he would keep trying to convince Trump of its merits.
But on Thursday, Abe said he would consider the possibility of Tokyo and Washington hammering out a trade deal alone -- Trump has said he preferred bilateral trade agreements to multilateral accords.
Abe was the first world leader to rush to meet the US president-elect in New York, visiting Trump just nine days after Americans voted him into office in a surprise victory.
The meeting stirred controversy when Trump's daughter, Ivanka, a former model and current business executive with no formal role in Trump's presidency, was seen in attendance.
Trump will also speak Saturday with German Chancellor Angela Merkel, Russian President Vladimir Putin, French President Francois Hollande and Australian Prime Minister Malcolm Turnbull.
The conversations come one day after Trump's meeting with Britain's Prime Minister Theresa May, the first foreign leader to visit his White House.
Trump hailed the "most special relationship" between the twin Atlantic powers and praised Britain's decision to leave the European Union as a "wonderful thing."