* U.N. rights boss urges restraint on all sides in Xinjiang

* Navi Pillay calls for full investigation into rioting

* Detainees entitled to humane treatment and fair trials

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By Stephanie Nebehay

GENEVA, July 7 (Reuters) - The top United Nations human rights official on Tuesday called on Chinese authorities and ethnic groups in the Muslim region of Xinjiang to refrain from further violence after what she called "a major tragedy".

Navi Pillay, U.N. High Commissioner for Human Rights, said demonstrators had the right to protest peacefully and that those arrested should be treated in line with international law.

A full, transparent investigation should be conducted into the causes of Sunday's deadly rioting, she said, and called on the authorities to identify the victims and establish precisely what happened to them to prevent a vicious cycle of unrest and retribution.

"I urge Uighur and Han civic leaders, and the Chinese authorities at all levels, to exercise great restraint so as not to spark further violence and loss of life," Pillay said in a statement. "This is a major tragedy."

Riot police on Tuesday fired tear gas to disperse rock-throwing Han and Uighur protesters who clashed in the capital of China's northwestern region of Xinjiang two days after ethnic unrest left 156 dead and more than 1,000 wounded.

"This is an extraordinarily high number of people to be killed and injured in less than a day of rioting," Pillay said.

Thousands of angry Han Chinese, many of them armed and seeking vengeance for deaths in the rioting, surged through Urumqi looking for Uighur targets on Tuesday.

Pillay's remarks voicing alarm at the high loss of life were the strongest yet by the world body. Her office does not have a a presence in China, despite years of seeking permission.

Chinese authorities have a duty to maintain public order, according to Pillay, a former U.N. war crimes prosecutor.

"However, it is vital that the authorities only resort to lethal force when it is strictly unavoidable in order to protect life."

The South African, who took up the top U.N. rights job last September, said China must treat detainees humanely and use methods of interrogation that adhere to international norms.

Any trials must be fair and sentences handed down proportionate for those found guilty of committing crimes. (Editing by Sonya Hepinstall)

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