BEIJING, China (CNN) -- After more than a week of protests against what some Chinese see as the demonization of their nation by the West, there are indications the Chinese government is making an effort to rein in the anger.
Supporters wave Chinese flags during Indonesia's leg of the 2008 Beijing Olympic torch relay in Jakarta Tuesday.
The protesters have mostly been angry young men, their fury directed against the French supermarket chain Carrefour and against CNN. Some protests, on mainland China and elsewhere, have drawn thousands.
However, Beijing appears to be gently admonishing protesters that enough is enough.
The state-run English-language newspaper China Daily for a fourth straight day on Tuesday called on protesters to tone it down.
"A stubborn insistence that those who do not join the protests and boycott Carrefour are not patriotic is false patriotism," the newspaper said in an editorial. "Patriots are supposed to adopt a tolerant attitude toward others and be broad enough to see what is good and what is bad in them.
"Over-the-top nationalism is not constructive, but can do harm to the country. If we want to improve things, we will have to encourage responsible patriotism." Watch how the government is trying to ease anger »
Carrefour became a target for protesters after anti-Chinese protests disrupted the Olympic torch relay in Paris earlier this month. Jin Jing, a disabled athlete, used her body to protect the torch as a pro-Tibetan demonstrator tried to grab it during the incident. Blog and text messages called on the Chinese to boycott French goods and businesses, particularly Carrefour.
The Chinese alleged on blogs and message boards that Carrefour had backed the Dalai Lama, the exiled Tibetan spiritual leader. Carrefour CEO Jose-Luis Duran, in an interview with the French weekly Journal de Dimanche, denied that, saying, "Carrefour has not given any direct or indirect support to any political or religious cause," according to a story on Forbes.com. Carrefour also put out a separate statement last week saying it has always supported the Beijing Olympics, according to the article.
The Chinese were already angry at Western media, including CNN, for what the government claimed was biased reporting over the recent Tibetan riots. CNN gained renewed focus for protesters after commentator Jack Cafferty called the Chinese "goons and thugs" and said the nation manufactures "junk."
Cafferty and CNN have clarified that his remarks were directed at the government, not the Chinese people. But the Chinese Foreign Ministry has said CNN did not go far enough and lodged a protest with the network's Beijing bureau.
Meanwhile, protesters' anger has continued to simmer. One moderate Chinese blog urges readers to boycott Carrefour "until the French give up their stupid ideas, until they bow their head."
An online petition started by the Legal Immigrant Association, a California-based nonprofit group dedicated to employment-based immigrant professionals, demands that CNN discipline Cafferty and apologize to the Chinese people. As of Tuesday, more than 101,000 people had signed it.
On Saturday, about 1,500 pro-Chinese demonstrators gathered outside of CNN's Los Angeles bureau to protest Cafferty's remarks, while other protesters gathered at the Time Warner headquarters building in New York..
Foreign Ministry spokeswoman Jiang Yu said Tuesday that while protesters' patriotism is "touching ... I believe they can be rational."
China's government has dealt with violent protests in the past. Three years ago, a spat with Japan triggered anti-Japanese riots across the nation. After a few days, Beijing clamped down on the violence.
The Beijing Olympic Games kick off in August, and they are of major importance to China.
"For some Chinese, they will tell you it's the most important event since 1949 -- since the creation of the PRC (People's Republic of China)," said Jean-Pierre Cabestan of Hong Kong Baptist University. "I think they are investing a lot in it because it's one of the first occasions for China to be among the big nations."
Asked whether the anti-Western online sentiment might affect attendance at the Games, Jiang said, "We will certainly adopt an open and warm posture to welcome people from all over the world for the Olympics. I think the Chinese people will show everyone a good spirit."
One Chinese blogger has launched a forum asking readers not to boycott Carrefour, arguing the store sells Chinese goods and has nothing to do with Tibet.
However, angry protesters seem to be slow to come around. According to a spot check, disagreements on the posting outnumber agreements more than six to one. E-mail to a friend
CNN's Hugh Riminton and Wen-Chun Fan contributed to this report.
All About China • Tibet
A pro-Tibetan protester in Paris attempts to wrangle the Olympic torch from Chinese fencer Jin Jing, who has become a national hero to many because of the incident. 
After anti-France protests were held in major Chinese cities over the weekend, China and France are now attempting to smoothen relations. China has discouraged the actions of the "radical" protesters, and French President Nicolas Sarkozy sent a letter to a Chinese Olympic athlete who has gained national fame in China following a controversial incident in the Paris Olympic torch relay.

At a press conference on Tuesday, Chinese Foreign Ministry spokeswoman Jiang Yu said the demonstrations were "encouraging and touching," but added that "we do not agree with some people's radical actions." She added that China should continue to harbor friendly bilateral relations with France.
A Carrefour retail store in China. Many Chinese protesters called for a boycott of Carrefour, who they accused of supporting the Dalai Lama. 
The Chinese state-run newspaper China Daily expressed the government's views on the protests in an editorial, warning against "false patriotism" and encouraging tolerance of differing opinions. "Over-the-top nationalism is not constructive, but can do harm to the country," the English-language newspaper said. "If we want to improve things, we will have to encourage responsible patriotism."

Some Chinese protesters have called for a boycott of French goods, in particular the French retailer Carrefour, which Chinese bloggers accused of supporting the Dalai Lama. Carrefour denied this allegation, saying in an interview that "Carrefour has not given any direct or indirect support to any political or religious cause."

The protests in China were a reaction to pro-Tibetan demonstrations held in Paris on April 7, when the Olympic torch was making its journey through the French capital. Pro-Tibet activists disrupted the torch relay by attempting to extinguish the flame or otherwise halt the proceedings. 

One of the more controversial incidents of the torch relay involved Chinese Olympic fencer Jin Jing, who was one of the athletes chosen to bear the torch. Protesters tried to wrestle the torch from wheelchair-bound Jin, who is now regarded by many Chinese as a national hero because of the incident.

French President Nicolas Sarkozy sent a letter to Jin, condemning the attack she suffered and praising her courage. "I would like to express to you my deep feeling towards the way you were shoved in Paris on April 7 when you were holding the Olympic flame. You showed an outstanding courage, which honors you, and all your country," Sarkozy wrote in the letter. He also extended a personal invitation to her.

"This friendly move by President Sarkozy is appreciated by the Chinese people," said ministry spokeswoman Jiang Yu. The letter was personally delivered by French Senate President Christian Poncelet, who is scheduled to meet with Chinese President Hu Jintao and other Chinese leaders this week. Former French Prime Minister Jean-Pierre Raffarin is also scheduled to visit China.