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A photo of a young girl holding a Chinese flag is one of many that China’s online censors have deleted over the last few days in an effort to quell nationalist support for ethnic Chinese rebels in Myanmar.

Others have depicted looted storefronts and bodies of civilians, some dead, some wounded, seeking shelter.

Dozens of soldiers and rebels have died since fighting erupted in the Kokang region near the Chinese border last week, according to the state-backed newspaper Global New Light of Myanmar.

Tens of thousands of refugees fleeing into China and an appeal for help from the rebel forces in Myanmar have now turned the hostilities into a delicate matter for the Chinese government. The Kokang region is largely populated by ethnic Chinese.

Peng Jiasheng, an ethnic Chinese who was affiliated with the now defunct, formerly China-backed Communist Party of Burma, leads the rebel forces in Kokang, who call themselves the Myanmar National Democratic Alliance Army.

Mr. Peng ruled Kokang until his ouster in an attack by the Myanmar armed forces in 2009 and has since lived in hiding.

A day into an attack by his rebel forces last week that ignited the hostilities, the 85-year-old appealed for support from all those of “common race and roots,” in an open letter widely circulated on social media.

“How is it possible that more than a hundred years after the Opium War, there are still more than 200,000 Chinese suffering under ethnic discrimination?” he wrote. “Every time Jiasheng is reminded of this situation, he bursts into tears, and the pain is unbearable.”

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Some Chinese microbloggers have responded to his call by likening his struggle to retake Kokang to the fight of Russian separatists in Ukraine, where Russia annexed the Crimean Peninsula last year.

“Let us help Kokang,” one Weibo user commented, while sharing the photo of the flag-holding girl. “The beasts of the Myanmar Army are continuing to slaughter Kokang’s Chinese in Laukkai,” another one wrote, sharing a photo of corpses in the city that has seen most of the fighting. Both those posts and many similar ones have since been deleted from Chinese microblogs.

In a Lunar New Year’s message released on Wednesday, the rebels’ military commander in charge of operations, Peng Deren, thanked Chinese Internet users for their support over the last year, along with Kokang residents and allied armed rebel groups. “The coming of spring brings back us wanderers’ desire to return home,” he wrote. Mr. Peng is the son of the rebel leader Peng Jiasheng.

Chinese state-affiliated news outlets were quick to denounce references to Crimea. “Those who are stuck in such comparisons are either spouting nonsense, or have ulterior motives,” Global Times, a state-run newspaper, wrote in an editorial on Monday.

“Varied forces in Chinese society should stay sober and avoid any premature stance or interference in northern Myanmar affairs, so as not to affect the government’s diplomacy,” the editorial argued.

A Chinese Foreign Ministry spokeswoman, Hua Chunying, echoed the sentiment at a regular news conference on the same day. China “does not allow any organization or individual to spoil China-Myanmar relations and undermine stability of the border area on the Chinese territory,” she said.

More than 30,000 people have crossed the border into China since the fighting began, Xinhua, the state-run news agency, has said.

The outpouring of support from Chinese citizens has been overwhelming for some residents of China. Lin Sen, who lives in Yunnan Province, across the border from Myanmar, said he had harbored up to 20 refugees at his home and had been flooded with phone calls from people wanting to help refugees.

“I tell people that there is no need to send supplies,” he said. “There is no shortage at the moment.” Some callers, he said, even contacted him from post offices, asking him for his address to mail emergency supplies.

On Tuesday, Myanmar imposed three months of martial law in the region. Fighting continued as of Friday, residents said. “They are still exchanging fire,” Li Jiapeng, who volunteered distributing aid to refugees on the Chinese side of the border, said by telephone.