President Biden and Chinese leader Xi Jinping signaled an effort to repair strained relations between Washington and Beijing, instructing officials to resume talks on major global issues, even as the two countries acknowledged areas of deep disagreement that could stymie efforts to improve relations.

The two leaders’ first in-person meeting since Mr. Biden became president lasted about three hours, including a break. It came after months of high tensions resulting from House Speaker Nancy Pelosi’s August visit to Taiwan and widening differences on a variety of issues, including Russia’s invasion of Ukraine and trade.

According to people familiar with the situation, any visits by senior US politicians to Taiwan could be viewed as provocative by the Chinese, raising the possibility of clashes between the superpowers. House Minority Leader Kevin McCarthy (R-Calif.) has stated that if elected Speaker, he will travel to Taiwan. Republicans are getting closer to regaining control of the House.

Mr. Biden stated at a press conference following the meeting that he does not believe China will attempt to invade Taiwan anytime soon and that the United States’ long-standing policy toward the island has not changed. During his discussions with Mr. Xi, he voiced his opposition to what the White House described as China’s coercive and increasingly aggressive actions toward Taiwan.

Mr. Biden described Mr. Xi as direct and straightforward, and he believes the Chinese leader is willing to compromise on some issues, though he did not specify which ones. He stated that he attempted to communicate his intentions to Mr. Xi in order to avoid miscommunications that could inflame tensions.

The talks on Monday signaled the reopening of communication lines between the two sides, which had been largely severed following Mrs. Pelosi’s visit to Taiwan. Beijing responded to the visit by conducting military drills, suspending climate talks and a wide range of law-enforcement cooperation with the US, and canceling some two-way military talks.

According to the White House, the two leaders have given senior officials authority to deepen talks. Mr. Biden also directed Secretary of State Antony Blinken to visit China to follow up on the meeting on Monday.

After Messrs. Biden and Xi decided to work toward an in-person meeting during a July phone call, the two countries planned the talks over several months and dozens of hours of negotiations. While this was Messrs. Biden and Xi’s first face-to-face meeting as their countries’ top leaders, the two have had five virtual or phone meetings since last year and extensive interactions when they served as vice presidents of their respective countries.

During the meeting, President Trump brought up the cases of American citizens detained in China. He also expressed concern about China’s treatment of ethnic Uyghurs and other Muslim minorities in Xinjiang, as well as the suppression of civil liberties in Hong Kong.

According to the White House, the two leaders agreed that “a nuclear war should never be fought and can never be won,” and they “emphasized their opposition to the use or threat of use of nuclear weapons in Ukraine.” Though Mr. Xi has previously expressed concern about the use of nuclear weapons in Ukraine, officials said the White House was eager for the Chinese president to reiterate that position during the meeting.

Mr. Xi also reiterated China’s support for peace talks between Russia and Ukraine, and expressed optimism that the United States, the European Union, and the North Atlantic Treaty Organization will begin comprehensive talks with Moscow.

Mr. Xi was elected to a record-breaking third term as Communist Party leader in late October, when he also promoted loyalists to the party’s highest levels. The personnel shuffle is expected to last until China’s annual legislative session in the spring, when top state positions, including the premiership and other cabinet positions, will be formalized.

Mr. Xi attended Monday’s meeting with newly empowered members of his leadership. U.S. officials said they saw the meeting as an opportunity to get greater clarity on points of contact in the Chinese government, gain new directives from Mr. Xi to re-engage with the Biden administration and possibly lay the groundwork for future conversations between the two leaders.