* G7 tells Beijing to respect rights in Xinjiang

* G7 calls for preservation of Hong Kong freedoms

* G7 urges study in China on COVID origins

* Expresses concern over situation in East and South China Seas

* G7 calls for peace in Taiwan Strait

* China: 'small' groups don't rule the world (Adds Biden comments)

By Guy Faulconbridge and Steve Holland

CARBIS BAY, England, June 13 (Reuters) - Group of Seven leaders on Sunday scolded China over human rights in its Xinjiang region, called for Hong Kong to keep a high degree of autonomy and demanded a full and thorough investigation of the origins of the coronavirus in China.

After discussing how to come up with a unified position on China, leaders issued a highly critical final communique that delved into what are for China some of the most sensitive issues, including also Taiwan.

The re-emergence of China as a leading global power is considered to be one of the most significant geopolitical events of recent times, alongside the 1991 fall of the Soviet Union that ended the Cold War.

China's rise has also unnerved the United States: President Joe Biden casts China as the main strategic competitor and has vowed to confront China's "economic abuses" and push back against human rights violations.

"We will promote our values, including by calling on China to respect human rights and fundamental freedoms, especially in relation to Xinjiang and those rights, freedoms and high degree of autonomy for Hong Kong enshrined in the Sino-British Joint Declaration," the G7 said.

The G7 also called for a transparent, expert-led Phase 2 COVID-19 Origins study including in China, to be convened by the World Health Organization (WHO). Reuters earlier reported the finalised version of the draft communique.

"We haven't had access to the laboratories," Biden told reporters.

Biden said it was not yet certain whether or not "a bat interfacing with animals and the environment... caused this COVID-19, or whether it was an experiment gone awry in a laboratory".

Before the G7 criticism emerged, China pointedly cautioned G7 leaders that the days when "small" groups of countries decided the fate of the world were long gone.

The G7 also underscored "the importance of peace and stability across the Taiwan Strait, and encourage the peaceful resolution of cross-Strait issues".

"We remain seriously concerned about the situation in the East and South China Seas and strongly oppose any unilateral attempts to change the status quo and increase tensions," they said.