CHINATOPIX, via Associated Press

Protesters burned a replica of the Japanese flag at a protest in Wuhan, in central China, on Sunday.

BEIJING — Anti-Japan demonstrators took to the streets again Sunday in cities across China, with the government offering mixed signals on whether it would continue to tolerate the sometimes violent outbursts.

The protests were orderly in Beijing, with several hundred people circling in front of the Japanese Embassy demanding Chinese control over a small island group known as Senkaku in Japan and as Diaoyu in China. Protests were also reported in several other cities, including Shanghai, Guangzhou and Qingdao.

On Saturday, protests occurred in more than 50 cities, with some violence reported. In Qingdao, a factory for the Panasonic Corporation was set on fire and a Toyota dealership was looted, according to pictures on social media sites and local residents reached by telephone.

“Across China, calls have grown for boycotts of Japanese products. Many Japanese retailers and restaurants have been forced to place signs in their windows supporting China, and on Sunday, Japan’s prime minister called on China to protect Japanese people and property.

A signed editorial on the Web site of People’s Daily, the authoritative Communist Party mouthpiece, said the protests should be viewed sympathetically. While not defending the violence, the editorial said the protests were a symbol of the patriotism of the Chinese people.

“No one would doubt the pulses of patriotic fervor when the motherland is bullied,” the editorial read. “No one would fail to understand the compatriots’ hatred and fights when the country is provoked; because a people that has no guts and courage is doomed to be bullied and a country that always hides low and bide its time will always come under attack.”

Some articles in the Chinese media, however, said the protests should be “rational” and peaceful.

On Monday, Defense Secretary Leon E. Panetta is scheduled to visit Beijing, and some observers said the government might try to limit the protests.

Just before landing in Tokyo on Sunday, Mr. Panetta told correspondents aboard his jet that he worried that territorial disputes in the Pacific could move from tension to conflict.

“I am concerned that when these countries engage in provocations of one kind or another over these various islands, that it raises the possibility that a misjudgment on one side or the other could result in violence,” Mr. Panetta said.

Mr. Panetta said the United States was not taking sides in any of the region’s territorial disagreements, but advocated using diplomacy to peacefully resolve them. One option, he said, would be for feuding nations to follow a code of conduct advocated by the Association of Southeast Asian Nations.

Both China and Japan claim the disputed islands, although Japan has controlled them for over a century. Beijing increase it pressure on Tokyo after the Japanese government purchased the islands from private owners. Japan says the move was to prevent nationalists from using the islands, but China has seen it as a step to solidify Japanese control. In response, China dispatched surveillance ships to the waters near the islands.

China’s state-run media has been ablaze with calls for the islands to be given to China, which claims that it controlled the islands before Japan’s colonial expansion in the late 19th century. Both countries have territorial disputes with other countries over island chains, some of which are thought to have rich natural resource deposits in the surrounding waters.

Evidence arose Sunday that some government officials were directly involved in the protests. In the western city of Xi’an, Chinese Internet activists identified one of the officials as the city’s police chief. Although localized riots and protests are common in China, organized, planned protests that are tolerated by the authorities are rare. .

The political analyst Li Weidong said the official tolerance fit a longstanding pattern of behavior in which Chinese governments use mass protests to further foreign policy goals. In a text message sent to friends and associates, Mr. Li compared the current protesters to the Boxers, a quasi-religious group that was used by the Qing dynasty to oppose foreign incursions.

“Beijing dares not to fight, but it’s unable to talk it over either,” Mr. Li wrote. “So it has to employ Boxers, using product boycott to press Japan.”