The world’s two most powerful leaders — Presidents Biden and Xi — skated and danced around their differences Monday, resolving, if nothing else, not to go to war while yielding little of substance on anything.

Mr.  Biden afterward acknowledged they had not really resolved much, saying, “I’m not suggesting this is kumbaya” — an African-American spiritual term that has come to mean overly optimistic or hopeful.

Most incredible was how they avoided gouging each other on Taiwan, while not budging from well-known policies. Mr. Biden, during a conversation of about three hours, accused China of “coercive and increasingly aggressive reactions” on Taiwan.

He was referring to Mr. Xi ordering war games by air, land, and sea during and after Speaker Pelosi’s visit to the island province. Mr. Xi countered, with equal bluntness, that Taiwan was not only at “the core of China’s core interests” but “the foundation in the China-US relationship.”

Mr. Xi even called the Taiwan issue “a red line that cannot be crossed” — echoing Mr. Biden’s remark several days ago that he hoped his meeting with Mr. Xi would establish “red lines” beyond which China should not go.

Having dispensed with their rhetoric on Taiwan, however, neither Mr. Biden nor Mr. Xi hinted at any possibility of going to war for the island, which Communist China has been claiming as its own ever since the victory of Mao Zedong’s Red Army on the mainland in 1949.

At a news conference afterward, Mr. Biden said he did not think “there’s any imminent intent” of China to invade Taiwan. In that spirit of non-menacing give-and-take, both presidents reflected a confidence born of their recent successes at home.

Mr. Xi has smoothly opened a third five-year term as China’s omnipotent leader, while Mr. Biden was heartened by the midterm elections, in which the Democratic Party retained control of the Senate and won key contests for governors.

The summit on the Indonesian island of Bali, a prelude to the G20 meeting of leading economic powers opening tomorrow, was Mr. Biden’s first meeting as president with Mr. Xi. The two have spoken by telephone five times over the past year and a half. This, though, was a chance to clear the air on a number of pressing issues.

The conversation was “open and candid,” Mr. Biden said afterward, adding that he was “not looking for conflict” but ways to “manage competition.” There was no need “for a new Cold War,” he said in response to a reporter’s question, though he and Mr. Xi were “very blunt with one another.”

The impression of what really got done, though, was not much  beyond the sense that neither wanted to be enemies. They agreed, as fully expected, that nuclear war should not be an option and they should cooperate on issues including climate change, hunger, and health.

On all such issues, Mr. Biden said, America is ready to “work with you if that’s what you desire,” and the two countries could get down to nitty-gritty details in future talks between Cabinet-level ministers and their aides. He was, he said, “committed to keeping the lines of communication open.”

The nuclear issue came up as Mr. Biden pressed Mr. Xi on China’s support for Russia in the war in Ukraine. They both said they believed “a nuclear war should never be fought” — not a remarkable view since President Putin has already said he would not use nuclear weapons in Ukraine.

There was no such reassurance on North Korea, whose leader, Kim Jong-un, has menaced his enemies with numerous missile tests and may be planning the North’s seventh nuclear test. Asked if Mr. Xi might dissuade the North, Mr. Biden said frankly that it was “difficult to determine whether China has the capacity” to wield such influence over the North.

There was no clear answer from Mr. Xi on such issues as Americans held as prisoners in China or on the issue of human rights, particularly the oppression of Tibet and the Uighurs in Xinjiang Province.

Rather, the tone was all to give an impression of a full and frank airing of views that did not quite live up to those expectations. Mr. Xi, greeting Mr. Biden, said he looked forward to bringing China-U.S. relations “back to the track of health and stable development,” and Mr. Biden said he hoped they would “manage our differences.”