TAIPEI (Reuters) - China are the real hackers not Taiwan and accusations from Beijing of a Taiwanese hacking group are fake news, senior government officials said in Taipei on Tuesday.

China's national security ministry said on Monday a Taiwan military-backed hacking group called Anonymous 64 has been carrying out cyberattacks against targets in China, urging people to report "anti-propaganda sabotage."

It also named three Taiwanese it said were part of the group and published their pictures.

Democratically governed Taiwan, which China claims as its own territory, frequently complains it is a victim of Chinese hacking and disinformation, but it is rare for Beijing to turn the tables and make the accusation back at Taipei.

Speaking to reporters at parliament, Taiwan Defence Minister Wellington Koo said it was China who was the main hacker around the globe.

"China is the first country when it comes to daily cyber attacks, doing it against Taiwan and countries with similar democratic ideals. They are the real originators," he said.

China's accusations are untrue, Koo added.

"As for what they have publicised, the military has the conviction to defend the country and will not shirk from doing so because of this, and nor will it have a chilling effect."

Also speaking at parliament, Premier Cho Jung-tai said China was spreading fake news to attack Taiwan.

"We must respond forcefully to fake news accusations against us," Cho said.

China has never renounced the use of force to bring Taiwan under its control. Taiwan's government rejects Beijing's sovereignty claims, saying only the island's people can decide their future.

China detests Taiwan President Lai Ching-te and calls him a "separatist". It has rebuffed Lai's repeated offers of talks.

(Reporting by Ben Blanchard; Editing by Christian Schmollinger)