Rupert Murdoch's News Corp wants Australia to break up Alphabet-owned Google.

In a report submitted to the country's competition watchdog, the media group's Australian unit wrote the U.S. tech giant wields "overwhelming market power," calling it the "most important gateway to the internet" and a vital platform for digital advertisements.

"Google leverages its market power in both general search services and ad tech services to the detriment of consumers, advertisers and news publishers," News Corp wrote in its submission to the Australian Competition and Consumer Commission.

Among a list of recommendations News Corp proposed to the competition watchdog for tackling the "harm" caused by digital platforms, it said Google should be made to sell off a part of its business.

"To remedy these harms, Google could either sell Google Search, or retain Google Search and divest the rest of its businesses to a third party," the report said. News Corp owns several big news publications including The Wall Street Journal and The Times newspaper in the U.K.

Even if the government in Canberra were to take News Corp's suggestion, it was not immediately clear how Australia could force the American tech giant to break up.

A Google spokesperson said the company has no comment on News Corp's recommendations, directing CNBC to an earlier blog post.