Japanese Prime Minister Shinzo Abe said Sunday he and U.S. President Donald Trump agreed to continue working closely toward North Korea's denuclearization, kicking off his busy five-day diplomatic schedule in New York.

After dinner with Trump, Abe said he had a "very constructive" discussion over trade and that the two leaders will take the topic up again when meeting as scheduled on Wednesday.

(Photo courtesy of Japan's Cabinet Public Relations Office)

"We agreed to make the momentum created in the historic U.S.-North Korea summit in June even stronger and to continue to coordinate closely toward the denuclearization of the Korean Peninsula," Abe told reporters after dining at Trump Tower.

Abe said Trump listened closely when he conveyed a message from family members of Japanese nationals who were abducted to North Korea in the 1970s and 1980s.

Dining with Trump was the first event on Abe's schedule after arriving in New York on Sunday. The bilateral alliance has been at the heart of Japan's diplomatic efforts, and Abe, who recently secured another three-year term as head of the ruling Liberal Democratic Party, is expected to stress its importance.

Before dining with Abe, Trump tweeted that he would be "talking military and trade. We have done much to help Japan, would like to see more of a reciprocal relationship. It will all work out!"

Abe said they exchanged candid views on various topics related to U.S. trade policy during their meeting that lasted over two and a half hours, adding, "We had a very constructive discussion on trade and investment between Japan and the United States."

Abe and Trump have built a rapport, but uncertainty remains over whether the Japanese leader can use it to leverage trade issues. Washington seeks a bilateral deal to correct what Trump sees as a trade imbalance between the two nations.

(Abe speaks to reporters after dinner with Trump)

Japan's economic revitalization minister Toshimitsu Motegi and U.S. Trade Representative Robert Lighthizer will meet Monday in New York to lay the groundwork for the Abe-Trump summit.

Abe's visit comes after the inter-Korea summit last week kept hopes alive for progress on North Korea's denuclearization.

North Korean leader Kim Jong Un pledged to dismantle his country's major nuclear facility if the United States takes reciprocal actions, and to close its key missile test site in the presence of international experts.

Japan has been coordinating closely with the United States toward the shared goal of denuclearizing North Korea, and Abe is expected to express support for Trump's possible second meeting with

Kim. Abe also plans to sit down with South Korean President Moon Jae In during his stay through Thursday.

Abe's week will be busy with high-level meetings aimed at addressing international issues ranging from the Syrian civil war and the Rohingya refugee crisis to U.N. sustainable development goals and climate change.

(Photo courtesy of Japan's Cabinet Public Relations Office)