* Row shows fragility of Sino-Japanese relations
* Japan govt criticised for "caving in" to China
* Four Japanese nationals still detained in China (Recasts first paragraph, adds Japan PM quote)
By Lucy Hornby and Chisa Fujioka
BEIJING/TOKYO, Sept 26 (Reuters) - Japan's prime minister on Sunday rejected China's demand that Tokyo apologise and compensate for detaining a Chinese fisherman, and said both sides must try and cool down their bitter feud.
The row has bounced back and forth between the two sides with demands for an apology and rejections, illustrating the fragility of ties between Asia's two biggest economies troubled by Chinese memories of wartime occupation, military mistrust and maritime territorial disputes.
The dispute also raised concerns about damage to Sino-Japanese trade ties at a time when Japan is becoming increasingly reliant on China's dynamism for growth.
Fishing trawler captain Zhan Qixiong was released and arrived back in China on Saturday after his boat collided with Japanese patrol ships on Sept 7 near disputed islets, known as the Diaoyu in China and Senkaku in Japan. His crew had been freed earlier.
The waters are believed to be rich in oil and natural gas.
Japanese Prime Minister Naoto Kan repeated that Tokyo would not respond to Chinese demands for an apology.
"Senkaku is a Japanese territory. From that point of view, apology or compensation is unthinkable," he told reporters. "I have no intention at all of meeting (the demand)."
But he also urged a return to calm.
"Both sides should first become calm and (then) deepen mutually beneficial strategic ties," he said. "What is necessary is for both to calm down and act based on a broad perspective." <^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ For factbox on China-Japan ties: [ID:nTOE68J014] For a factbox on frictions with China: [ID:nSGE68N028] For Q+A on the gas dispute: [ID:nSGE68G07N] For a company view on business ties: [ID:nSGE68L02G] For a map of the disputed islands click:
For a graphic comparing Asia's two largest economies:
Kan's government has come under fire from domestic media and ruling as well as opposition lawmakers for "caving in" to Chinese pressure by releasing the captain after China detained four Japanese citizens, although Japanese officials denied a linkage.
The four were detained on suspicion of violating the law regarding protection of Chinese military facilities, though the exact offence is not clear.
A former Japanese foreign minister said that international perceptions of China would be hurt by its refusal to back down.
"It was our territory and there was no fault in arresting him in accordance with the law," Katsuya Okada, secretary-general of the ruling Democratic Party and foreign minister until a Sept. 17 cabinet reshuffle, told public broadcaster NHK.
"There have been views that this affair was a complete defeat for Japan, but this was a loss for China. China showed the world what kind of a country it is."
A Japanese man was arrested in Nagasaki, western Japan, on Sunday after he threw what appeared to be a smoke flare into the grounds of the Chinese consulate general, Kyodo news agency said.
The consulate general was unstaffed, and no one was injured, Kyodo said, adding that police believed the incident could be related to the territorial spat.
Freed captain Zhan told China Central Television he was eager to return for more fishing. (Additional reporting by Kiyoshi Takenaka and Linda Sieg; Editing by Sanjeev Miglani: ((email@example.com; +86 10 6627-1269; Reuters Messaging: firstname.lastname@example.org))