Peter Greste. Photo: ABC/Twitter: @PeterGreste

Detained Australian journalist Peter Greste has released a letter vowing to fight for freedom of speech in Egypt after being jailed for reporting on unrest in the country.

The award-winning Al Jazeera reporter was arrested in Cairo on December 29 along with colleagues Mohamed Adel Fahmy and Baher Mohamed.

The trio had been reporting on the political turmoil in Egypt when they were accused of holding illegal meetings with the Muslim Brotherhood (MB).

Egypt's military-installed leaders declared the Muslim Brotherhood a terrorist organisation in December, and had previously accused Al Jazeera of pro-Brotherhood coverage.

The Al Jazeera network, however, has emphatically defended its staff's actions, saying they were doing their job by reporting objectively.

Greste, who is being held in Cairo's Tora prison, says Egyptian authorities are cracking down on anyone "who refuses to applaud the institution".

Greste says he had originally planned to fight for his freedom "quietly", in part not to risk the precious little recreational time he was given.

However, he now says acquiescence on his behalf would validate the Egyptian authorities' "attack" on freedom of speech.

"I have sought, until now, to fight my imprisonment quietly from within, to make the authorities understand that this is all a terrible mistake - that I've been caught in the middle of a political struggle that is not my own," Greste writes in the letter, which has been authenticated by his parents.

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Peter Greste declares battle for freedom of speech in Egypt after prolonged detention