Japan’s new leader infuriated Beijing. She isn’t backing down.

First, it was President Trump, who gushed on an October trip to Tokyo that she would prove to be one of Japan’s greatest leaders.

Next, it was Chinese leader Xi Jinping, who was infuriated by her remark that Japan would likely get sucked into a war if China made a move on Taiwan. Takaichi’s comment ignited an economic and political pressure campaign that has seen Beijing berate Tokyo at the United Nations, cancel tourist flights to Japan and threaten a ban on imports of Japanese seafood.

The result for Takaichi? Buoyant approval ratings for her month-old government.

“I think she did a good job. I’ve been waiting for Ms. Takaichi to speak up like that," said Mie Tanaka, who was enjoying the sunshine Saturday near the Tokyo Dome baseball stadium. She expects the spat will rumble on but said she isn’t worried about it. “I think we should just let China say what it wants," she said, adding that “Japan has the U.S. on our side."

Takaichi, 64 years old, took the reins in Japan in late October after winning the leadership of the ruling Liberal Democratic Party on what was her third attempt.

A conservative who favors blue jackets and a roomy handbag, she vowed on taking office to “work like a horse" to revitalize Japan’s economy and burnish the country’s global prestige.

Voters got an early display of that work ethic when Takaichi slept in a parliamentary dormitory and got to her office to begin work at 3 a.m. on Nov. 7. She later apologized to her security detail, secretaries and driver for inconveniencing them by starting at such an early hour.

That was the day she was swept into a diplomatic firestorm. Asked by an opposition lawmaker if a blockade of Taiwan would constitute a threat grave enough to Japan that it might deploy its military in self-defense, Takaichi said that it could.

“If it involves the use of warships and the exercise of force, I believe this is a case that could unquestionably constitute a crisis threatening the nation’s existence," Takaichi said.

Although she added that Japan’s longstanding position is that issues concerning Taiwan should be resolved peacefully, the damage was done.

China claims the self-governing island of Taiwan as its own and hasn’t ruled out taking it by force. Beijing’s apoplectic response to Takaichi’s perceived intervention in China’s affairs has included intense personal attacks on the new prime minister, often linking her with the militarism that fueled Japan’s brutal conduct in World War II.

One cartoon posted on X by Chinese state media depicted her in Japanese Imperial Army uniform, a sheathed sword at her side. Another had her torching Japan’s pacifist postwar constitution, releasing a fiery-eyed specter wearing Japan’s wartime rising-sun flag.

Such insults have extra bite because Takaichi’s appeal to conservative voters in Japan is based in part on her nationalist beliefs. As a young lawmaker, she was critical of former Prime Minister Tomiichi Murayama’s apology for Japan’s colonial expansion and its aggression in World War II, saying such a statement shouldn’t have been made without a broader national discussion. Like many other Japanese lawmakers, she has been a frequent visitor to Tokyo’s Yasukuni Shrine, where Japanese war dead, including some war criminals, are commemorated.

In attacking Takaichi, China is aiming to destabilize her fledgling administration, said Yinan He, an associate professor at Lehigh University in Pennsylvania and an expert in Sino-Japanese relations. Beijing is also firing a warning shot at Taiwan’s allies in Asia and ultimately the U.S., she said.

“In Chinese they call it ‘kill the chicken to scare the monkey,’" she said. “They will want to hurt Japan severely enough this time so that everyone else will be scared."

The diplomatic spat looks set to drag on. Japanese officials worry the economy could suffer if relations deteriorate further, especially if China chooses to squeeze Japan’s access to rare-earth minerals critical to manufacturing.

Still, the brawl hasn’t hurt Takaichi’s popularity. Polls suggest about seven in 10 voters approve of her government, more than double the support enjoyed by her predecessor, Shigeru Ishiba, on the eve of his resignation in September.

Some allies are rallying to her defense. Taiwan’s de facto embassy in Tokyo on Friday urged Taiwanese seafood lovers to buy all the Japanese scallops they can to counter Beijing’s threatened import ban.

“I just want to say directly from the president and from myself and from the embassy, for the prime minister, we have her back," U.S. Ambassador to Japan George Glass said Thursday.

Takaichi has given little indication that she is rattled by the bust-up. In a message on her official X account posted while she was en route to a gathering of world leaders in South Africa, she confessed to agonizing over her wardrobe. “Maybe I need to push myself and buy some outfits that would let me get the upper hand in diplomatic negotiations," she said.

Write to Jason Douglas at jason.douglas@wsj.com and Junko Fukutome at junko.fukutome@wsj.com