Story highlights Chinese ships briefly enter waters around the group of islands

Tensions between Japan and China are high over the disputed islands

Japan controls the islands, but China claims they are part of its territory

Thousands of Chinese protesters hurled bottles and eggs outside the Japanese embassy in Beijing over the weekend amid growing tensions between the two nations over a group of disputed islands.

Waving Chinese national flags and holding portraits of the late Chairman Mao Zedong, the mostly young protesters chanted "down with Japanese imperialism" and called for war as they made their way down the streets under the watchful eyes of police and guards.

Elsewhere in China, anti-Japanese rallies broke out in dozens of cities and sometimes turned violent. Messages and photos posted on Chinese social media sites showed angry mobs in numerous cities ransacking Japanese stores and restaurants as well as smashing and burning cars of Japanese make.

Japanese media also reported incidents of assault on Japanese nationals in China in the past few days. A Chinese foreign ministry spokesman insisted Friday that the public anger was not aimed at the Japanese people, whose safety would be protected in China according to law.

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Authorities rarely permit protests in China, prompting suspicion that Saturday's nationwide rallies were government-sanctioned. In Beijing, police walking along the demonstrators were seen to ask spectators to join in instead of blocking the street.

By Saturday night, China's state-run media had started appealing for restraint, running commentaries that condemned violence and lectured the public on the true meaning of patriotism. In a sign of rising concern over the gathering of large crowds, authorities in cities that had seen the most ferocious protests canceled entertainment and sporting events.

Tensions escalated Friday when Chinese maritime surveillance ships ignored warnings from Japan and briefly entered waters around the group of islands at the center of the heated territorial dispute.

The ships arrived near the uninhabited islands -- which Japan calls Senkaku and China calls Diaoyu -- and began patrols and "law enforcement," China's state-run news agency Xinhua reported.

The islands, situated in the East China Sea between Okinawa and Taiwan, are under Japanese control, but China claims they have been a part of its territory for ages.

The long-running argument over who has sovereignty has triggered protests in both nations.

The United States,a key ally of Japan, has repeatedly urged Tokyo and Beijing to resolve the dispute through dialogue. U.S. Defense Secretary Leon Panetta will meet with his counterparts in Japan and China this weekend, the Department of Defense said Thursday

Chinese vessels had all left the waters by Friday afternoon and headed north, the Japanese Coast Guard said.

Japan said it will intensify patrols of the area.

The controversial Chinese move to begin patrols around the islands follows Japan's purchase of several of the islands from a private owner this week. China described the deal as "illegal and invalid."

Animosity between the two countries over the islands runs deep.

They have come to represent what many Chinese see as unfinished business: redressing the impact of the Japanese occupation of large swathes of eastern China during the 1930s and 1940s.

China says its claim goes back hundreds of years. Japan says it saw no trace of Chinese control of the islands in an 1885 survey, so formally recognized them as Japanese sovereign territory in 1895.

Japan then sold the islands in 1932 to descendants of the original settlers. The Japanese surrender at the end of World War II in 1945 only served to cloud the issue further.

The islands were administered by the U.S. occupation force after the war. But in 1972, Washington returned them to Japan as part of its withdrawal from Okinawa.