Google has warned a copycat Chinese website to stop using a logo that resembles the US internet giant's or face possible legal action, state media reported.

The warning issued to the "Goojje" website comes as Google is contemplating its future in China after saying it would no longer obey government censorship rules and could pull out entirely over alleged cyberattacks.

Google accused Goojje of infringing on its trademark rights, saying the logo of the Chinese website could make users believe it was authorised by or linked to the US company, the Shenzhen Economic Daily reported.

In a letter sent to Goojje by Google's lawyers, the US internet firm demanded the Chinese site stop using the logo, the report said.

Google China did not immediately respond to a request for comment.

Reports have said Goojje was launched last month by a 20-strong team led by a college student identified only by the surname Wen, after Google issued its threat to pull out from China.

The operators of Goojje have posted vague statements on the website construed by some media as offering support for Google.

Goojje's homepage imitates Google's design and its Chinese name ends with a character that means "big sister". Google's Chinese name, meanwhile, ends with a character that is a homonym for "big brother".

Google said last month it would no longer abide by Chinese government censorship and was mulling leaving the country with the world's largest number of online users, citing cyberattacks on it and more than 20 other companies.

The Google row has added to tensions between Beijing and Washington on a range of other issues including trade, US arms sales to Taiwan, and Tibet.