President Trump pressed his personal brand of diplomacy as President Xi Jinping of China made his first trip to the White House in more than a decade. President Trump, Melania Trump, President Xi Jinping of China and Madame Peng Liyuan attended a state visit on Thursday.

President Trump said he had “never gotten along better” with President Xi Jinping of China amid military flyovers, gifts of pandas and lavish ceremonies that masked significant divides over artificial intelligence and trade. “President Xi and I both understand that we represent different systems but the ties between our people endure,” Mr. Trump said at the state dinner. “Together we can continue to build a relationship that promotes prosperity and security for future generations.”

Mr. Xi warned that the two countries should avoid the “Thucydides Trap.” “We do not need to avoid mentioning competition, but our competition should be a healthy one and should be kept within bounds,” Mr. Xi said. “It should be a race of catching up with one another, not a wrestle in which one either wins or loses. China and the United States must hold the line of no conflict and no confrontation between us.”

In private, the leaders discussed security, “super intelligence,” trade, Taiwan, the Middle East and Russia’s war in Ukraine. The nations extended a shaky trade truce by two months past a November deadline. Mr. Xi said A.I. must remain “always under human control,” while Mr. Trump called fears of mass extinction a “hoax.” Divides remained over election meddling, Iran, Tehran and American agriculture purchases.