Opinion editor's note: Editorials represent the opinions of the Star Tribune Editorial Board, which operates independently from the newsroom.

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This week's three-hour meeting between the leaders of the world's two most powerful countries was not a "kumbaya" moment, President Joe Biden said. And yet, he added, "I absolutely believe there need not be a new Cold War" with China.

For his part, Chinese President Xi Jinping also looked to stabilize relations despite a deep divide over Taiwan, Russia's brutal invasion of Ukraine, China's horrendous human-rights record, technology transfers and other issues.

"As the leaders of these two great powers, China and the United States, we must play the role setting the direction of the rudder, and we should find the correct approach for developing bilateral relations," Xi said, according to China's official summary of the high-profile presidential discussion that took place amid the G-20 Summit in Bali, Indonesia.

The warmer tone and tamping down of Cold War comparisons should not, however, eclipse the challenges that still threaten the world's most important bilateral relationship. In particular, China's increasingly assertive and even bellicose claims to Taiwan, which Xi characterized as "the core of China's core interests, the foundation of political foundations in the China-U.S. relationship and a red line that cannot be crossed in the China-U.S. relationship."

Xi's red line has been blurred by Biden, who yesterday reaffirmed America's longstanding "One-China" policy and the concept of "strategic ambiguity" over the U.S. response to a potential Chinese invasion of the island despite Biden unambiguously saying four times during his presidency that the U.S. would indeed come to Taiwan's defense under Chinese attack.

Overall, however, the two presidents "showed confidence in each other's ability to manage the increasingly fraught U.S.-China relationship," Ryan Hass, a senior fellow at the Brookings Institution, told an editorial writer in an email interview. "Even as neither leader gave ground or offered any concessions on issues of concern, they both signaled that they were determined to compete without resorting to conflict. They both agree on what needs to be avoided."

And, to some degree, what needs to be engaged, including renewed dialogue on the climate crisis. That's critical because China and the U.S. are the world's two biggest carbon emitters. Many vexing issues remain, however, including the export of sensitive technology, which the Biden administration has recently restricted even further.

Overall, "there was no shift in policy, but there was a shift in tone and a show of greater flexibility on both sides," Amanda Hsiao, senior analyst on China at the International Crisis Group, told an editorial writer via email. Writing from Taiwan, Hsiao added that, "China agreeing to restart dialogues without any apparent give from the U.S. suggests Beijing is approaching the bilateral relationship more pragmatically."

And more confidently. In fact, both leaders were bolstered by recent votes. Xi's recent ascension to a precedent-breaking third five-year term makes him the most powerful leader since Mao. Biden's success is more measured, of course, but his party's relative success in last week's midterm elections gives him more geopolitical clout.

"The domestic position both leaders have secured — particularly Xi — was likely a factor for both sides coming into the meeting with a greater willingness to negotiate, as both sides are more confident of their abilities to manage the domestic costs of appearing more conciliatory," Hsiao said.

One of many issues that Biden should not offer reconciliation on is Russia, and the readouts from each side suggest the disconnect is deep — and dangerous. Biden indicated that he and Xi "reaffirmed our shared belief" that the threat of using nuclear weapons is "totally unacceptable." Xi, according to Beijing's account, said that regarding the war in Ukraine "a complicated issue does not have a simple solution" and that "confrontation between major powers must be avoided." That's true, but hardly an unequivocal rejection of using nukes.

While China has not materially aided Russia's war, it's had its diplomatic back as the two nations shamefully pledged a partnership "without limits" just weeks before Russia's unprovoked invasion.

Xi's words "indicate Beijing is still balancing between its interest in maintaining its strategic alignment with Moscow and its interest in keeping its relationship with Washington stable," Hsiao said. But that balancing act can't last forever. China has chosen wrongly, aligning itself with war criminals. Biden is right to press Beijing and other recalcitrant capitals worldwide on this morally clear point.

Less clear is the next phase of U.S.-China relations. "The true measure of [the] meeting will be in where the relationship stands six months from now," Hass said. "Will there be a resumption of workmanlike efforts to manage tensions and pursue coordination on shared challenges? Or will there be further intensification of rivalry?"

Don't expect kumbaya, as Biden intoned. But avoiding another cold war would indeed benefit both nations — and the world.