President Trump on Sunday opens five days of high-wire summitry in Asia that will climax Thursday with the first face-to-face conversation of his second term with Communist China’s president, Xi Jinping.

Mr. Trump believes they can at last reach a viable understanding on tariffs and trade, notably the import of Chinese rare earth elements for electronics in products ranging from motor vehicles to computer screens. Mr. Trump is more confident after talks at Washington between the Treasury secretary, Scott Bessent, and China’s vice premier, He Lifeng.

Having previously said debating thorny trade issues with Mr. Xi would get nowhere, the president now says they can “work out a lot of our doubts and questions and our tremendous assets together.”

Mr. Trump will meet Mr. Xi at the South Korean city of Gyeongju the day before the gathering of the Asian-Pacific Economic Cooperation group that is drawing them and 19 other leaders to the ancient Korean capital. In what is expected to be a long session, the president will be looking for common ground on high tariffs he’s imposed while China inundates the world with its exports but threatens to hold back on rare earth.

Whatever comes out of the meeting, it will upstage the APEC talks that will go on for the next two days.  Mr. Trump, having seen Mr. Xi at Mar-a-Lago and on a state visit to Beijing during his first term, has talked to him by telephone twice during his second term. He began his second presidency by portraying China as America’s worst foe in Asia,  but he and Mr. Xi could lower the temperature even if they agree to disagree on key issues.

The prospect of the Trump-Xi summit is also likely to be the dominant topic of conversation on the sidelines of a meeting of the Association of Southeast Asian Nations in Malaysia, where Mr. Trump begins his diplomatic swing  Sunday. Messrs. Bessent and He will be talking to each other again at Kuala Lumpur.

Neither Mr. Xi nor Russia’s president, Vladimir Putin, will be at ASEAN, but  Mr. Trump will meet other world leaders, including Brazil’s left-leaning president, Luiz Inacio Luila da Silva, who would also like to persuade him to cut  tariffs. Hosting the summit, Malaysia’s prime minister, Anwar Ibrahim,  who pursues neutrality between Communist China and America and tolerates diplomatic relations with North Korea, will have a similar message.

At ASEAN, Mr. Trump will also meet  Japan’s newly ensconced prime minister, Sanai Takaichi,  but their first big conversation will have to wait until Tuesday, after he flies to Tokyo on the second leg of his Asian odyssey. Again, tariffs will be a big topic of conversation, but just as important will be their meeting of minds on the need for elevating defenses primarily against China — and also North Korea.

An ultra-rightist with distinctly hawkish views, Ms. Takaichi lived up to that reputation in her first major speech since her election by the parliament, or Diet.  Promising to raise Japan’s defense spending to 2 percent of its gross domestic product by early next year, she warned  of the “serious threat” posed by Communist China, North Korea, and Russia.

She would, she said, “build a direct trust relationship” with Mr. Trump while encouraging trilateral South Korean-Japanese-American “security cooperation” — a hallmark of relations between the three countries.