Mr. Trump plunged into a risky nuclear negotiation with North Korea’s Kim Jong-un, despite Mr. Abe’s warnings to hold a tough line with Pyongyang. Officials in Tokyo worry that a nuclear deal could hurt Japan, if Mr. Kim agrees to give up his intercontinental ballistic missiles, which can reach the United States, without surrendering his intermediate and short-range missiles, which can hit Japan.

In that regard, the impasse between Mr. Trump and Mr. Kim in Hanoi in February was positive news. Japanese officials were encouraged that Mr. Trump rejected Mr. Kim’s demand to lift onerous sanctions against North Korea in return for it shutting down an aging nuclear facility at Yongbyon. As long as Mr. Trump refuses such demands, analysts said, he and Mr. Abe will be on the same page.

What could be more challenging for Mr. Abe, in the short run, is persuading Mr. Trump to remain a visible presence at international gatherings, like the Group of 20 summit meeting, scheduled for the Japanese city of Osaka in June, as well as the Group of 7 meeting set for France in August and the East Asia Summit in Thailand. Japan, which assumed the G-20 presidency for the first time this year, views the gatherings as a crucial way to exercise diplomatic leverage.

Mr. Trump will visit Tokyo to meet the new emperor, Naruhito, in May, only a month before the Osaka summit meeting. He famously clashed with other Western leaders at his last Group of 7 meeting in Canada. And he sent Vice President Mike Pence in his stead to last year’s East Asia Summit in Singapore.

“The Japanese would be lucky to get Trump to one of the three,” said Michael J. Green, who holds the Japan chair at the Center for Strategic and International Studies. “They really need him to support the international institutions that underpin Japan’s own diplomatic position.”

On trade, the two sides appear to be heading toward a limited deal that would give American farmers and ranchers better access to the Japanese market, and Mr. Trump a political victory before the 2020 presidential election. The countries could then swing back later for a more comprehensive trade agreement covering manufacturing and services.

Mr. Trump indicated on Friday that a deal could be in the final stages by the time he heads to Japan.