In North Korea and Taiwan, President Biden faces two of the world’s most dangerous problems. His challenge is to convince potential adversaries that a politically divided United States is stronger than it looks.

Biden sounded a firm note on both fronts Thursday during his first formal news conference. He warned North Korea that “there will be a response” if it continues its recent missile tests, but he also offered “some form of diplomacy” with “the end result of denuclearization” of North Korea.

On China, Biden pledged “steep, steep competition,” by reinvesting in science at home and U.S. alliances abroad. But he also affirmed his personal relationship with President Xi Jinping, whom he called “a smart, smart guy.”

Biden’s performance on Thursday underlined that his priority, for now, is domestic reconstruction rather than foreign intervention. On Afghanistan, for example, he came close to setting a year-end deadline for withdrawing all U.S. troops, even though a political framework for power sharing and a cease-fire aren’t yet in place. This position will disappoint some of Biden’s military advisers, who favor an open-ended, conditions-based approach.

North Korea had delivered a fiery calling card over the past week by launching a series of short-range missiles. Biden initially dismissed the tests as “business as usual,” but he said yes when asked Thursday whether he agreed with former president Barack Obama that North Korea was the most important foreign policy issue. The president’s aides are debating how to frame a peace initiative that would take up where the Trump administration’s showy diplomacy left off.

North Korea offers a rare example of where President Donald Trump prepared carefully for a diplomatic pressure campaign. After just three months in office, Trump hosted Xi at his Mar-a-Lago Club — enlisting Xi as a diplomatic partner in squeezing North Korean leader Kim Jong Un. In the end, Trump got little to show for his leverage, except three meetings with Kim.

Biden has taken the opposite opening move with Xi’s China. Instead of sunny Palm Beach, Fla., the initial venue was the deep freeze of Anchorage. During the encounter last week between Secretary of State Antony Blinken, national security adviser Jake Sullivan and their Chinese counterparts, both sides sought to demonstrate resolve for what Chinese official media have called a period of “protracted struggle.”

Taiwan is where Chinese overconfidence seems most likely to produce a dangerous miscalculation. U.S. officials in Anchorage came away worried that Xi might be preparing to abandon the ambiguous but relatively stable status quo in Taiwan — described in the nearly 50-year-old formula of “one China” but two governments — in favor of a risky push for reunification.

Taiwan poses an interesting test of whether Chinese leaders really believe their rhetoric about American decline. If Xi thinks the United States’ demise is permanent and irreversible, the wise course presumably would be to wait until America is even weaker. But if Xi instead fears a U.S. rebound, then he might be tempted to act more quickly.

“China seems to be believing its own narrative about U.S. decline — thinking, ‘This is China’s moment.’ If they believe that, it raises the risk of miscalculation,” Michèle Flournoy, former undersecretary of defense in the Obama administration, warned this week. She was speaking Wednesday at a China forum hosted by the University of California at San Diego, which gathered many of the nation’s top Asia experts.

But Bonnie Glaser, a China scholar at the Center for Strategic and International Studies, took a more sanguine view. “Xi’s priority is to deter Taiwan’s independence, and China has achieved that objective, at least for the time being,” Glaser argued. “Reunification is a clear goal, but it isn’t an urgent priority. Xi is not willing to risk all his other domestic objectives to achieve it.”

For all of China’s newfound confidence, its leaders seem to want regular dialogue with the United States, rather than a sharp rupture. As diplomats Yang Jiechi and Wang Yi left the meeting with Blinken and Sullivan, they proposed a reciprocal meeting in China. “Thank you,” said Blinken, and the Chinese kept pressing (apparently without success) to find out whether that meant yes.

Since Anchorage, Chinese think tanks have been using a phrase that means “hit, hit, talk, talk” to describe what’s ahead with the United States, according to one top Sinologist. The “hit, hit” part of that formula carries significant risks — especially if China continues to believe that a weakened America isn’t ready to fight back.

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