During that trip, he met with Liu Jieyi, the director of China’s Taiwan Affairs Office, who flew from Beijing to the city of Shenzhen to meet him. He also met behind closed doors with the top Communist officials in Hong Kong and Macau, which are administered by China under “one country, two systems” arrangements that, at least in theory, give the territories a high degree of autonomy. In recent years, political freedoms in Hong Kong have been eroding under pressure from Beijing.

China’s leader, Xi Jinping, who in January vowed that the country would eventually take control of Taiwan, has offered similar semiautonomy to the Taiwanese people, hoping to entice them into peaceful unification. But poll after poll has shown that an overwhelming majority of Taiwanese reject a Hong Kong-style arrangement.

Huang Jie, a Kaohsiung city councilor, said it was troubling that Mr. Han had not voiced opposition to a “one country, two systems” model for Taiwan during his trip to China.

Ms. Huang is a member of the New Power Party, which grew out of a protest movement in 2014 that halted the Kuomintang’s plans to open Taiwan’s service sector to Chinese investment. In May, she questioned Mr. Han about his plan to establish a free economic zone in Kaohsiung, which critics say will give China greater influence in the city. Ms. Huang gained a measure of fame when a clip of her giving an eyeroll to Mr. Han, who appeared unable to explain details of his plan, went viral.

Since becoming Taiwan’s most famous city councilor, Ms. Huang said, she has received both an outpouring of support and a barrage of online criticism, much of it written in the simplified Chinese characters used in mainland China but not Taiwan. “You can tell it’s coming from China’s online army,” she said in an interview.

Ms. Huang said she was more concerned about Mr. Han becoming president than about the vitriol. “I don’t think he understands national security,” she said of Mr. Han. “If he becomes president, it will be a threat to our country.”

Kathy Hong, a marketing consultant and Kaohsiung native, said she believed Mr. Han’s biggest priority as mayor had been to promote his presidential aspirations. Ms. Hong said she and many of her friends feared the prospect of Mr. Han becoming president and signing an agreement with China that would give up Taiwan’s sovereignty.