Abe met with Cuban President Raul Castro during a visit that comes after Tokyo's close ally Washington restored ties with the communist island last year.
"I sincerely hope my stay here becomes an opportunity to open a new page in the relationship of friendship between both nations," Abe said in an interview published in the Cuban Communist Party's official newspaper, Granma.
The head of the world's third-largest economy called for "open dialogue" to stimulate trade and investment, development cooperation and tourism.
The Japanese premier is scheduled to hold a news conference today before departing the Caribbean island.
More From This Section
Japan was Cuba's second-largest trading partner between 1970 and 1985, but the relationship deteriorated drastically as the Cuban economy took a hit from the breakup of the Soviet Union, the country's key ally, in the early 1990s. Trade totaled about USD 35 million in 2014.
Abe said he also wanted to discuss nuclear disarmament.
On Monday, Cuba signed a debt restructuring deal with Japan according to which Tokyo will forgive part of Cuba's debt, leaving it to pay USD 606 million. Of that, USD 249 million is set to be deposited in an investment fund for Japanese businesses on the island, the Japanese government said.