Speaking in Amman, where Japan announced grants of up to 1.63 billion yen, about $15 million, to help Jordan support an influx of Syrian refugees, Mr. Abe said he planned to discuss “all aspects of the future development of relationships between Japan and China, and Japan and South Korea” at the meeting next week. He added that he would push for more “concrete actions” from North Korea to flesh out the commitment to denuclearization that Mr. Kim discussed with Mr. Moon in historic talks in the border village of Panmunjom last Friday.

Of the three leaders convening in Tokyo next week, Mr. Abe, who has lately been dogged by influence-peddling scandals at home, is perhaps most in need of a domestic boost. Undoubtedly, all three leaders will want to talk about advancing the North Korean peace process. But the unusual personality and style of President Trump is an equally urgent topic.

“A lot of the stimulus for this diplomacy in northeast Asia is certainly the North Korean threat,” said Mireya Solis, co-director of the Center for East Asia Policy Studies at the Brookings Institution. “But they are also dealing with this president, who is in so many ways changing the parameters of U.S. foreign policy.”

The meeting will provide an opportunity for the three leaders to discuss commercial ties, at a time when the United States is threatening a trade war with China and has recently renegotiated a two-way trade agreement with South Korea.

It will be the first visit to Japan by Mr. Moon since he was elected president last May, and the first visit to Tokyo by a South Korean president in more than six years. Mr. Li would be the first Chinese premier to visit Japan in eight years.