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.

"But after two weeks in prison it is now clear that this is a dangerous decision. It validates an attack not just on me and my two colleagues but on freedom of speech across Egypt.

"Our arrest is not a mistake, and as a journalist this is my battle. I can no longer pretend it'll go away by keeping quiet and crossing my fingers.

"I have no particular fight with the Egyptian government, just as I have no interest in supporting the MB or any other group here.

"But as a journalist I am committed to defending a fundamental freedom of the press that no-one in my profession can credibly work without. One that is deemed vital to the proper functioning of any open democracy, including Egypt's with its new constitution."

Al Jazeera journalists held in 'scorpion prison'

Greste is kept in his cell 20 hours a day, but says his detention is "relatively benign" compared to that of Fahmy and Mohamed, who, having been accused of being Brotherhood members, are being held in a so-called "scorpion prison".

"They are being held in the far more draconian 'Scorpion prison' built for convicted terrorists," he said.

"Fahmy has been denied the hospital treatment he badly needs for a shoulder injury he sustained shortly before our arrest.

"Both men spend 24 hours a day in their mosquito-infested cells, sleeping on the floor with no books or writing materials to break the soul-destroying tedium."

Greste says the trio have been accused of collaborating with a terrorist organisation, hosting Muslim Brotherhood meetings in their hotel room, and using unlicensed equipment to broadcast false information in favour of the Brotherhood and to discredit the Egyptian state.

However, he says Egyptian authorities have yet to present any evidence supporting the allegations and the men have not been formally charged with any crime.

Despite this, Greste says the prosecutor general has extended their detention by another 15 days to give investigators more time to build a case against them.

"He can do this indefinitely - one of my prison mates has been behind bars for six months without a single charge," he said.

Call for sustained pressure on Egyptian authorities

The trio have received widespread support, with US republican senator John McCain adding his voice to those calling for their release.

"I think it's a clear violation of not only their human rights but of any aspect of freedom of the press," Mr McCain said.

"For the Egyptian government to keep them in prison, I think, is another indicator that this military government, and really that's what it is... not keeping with the standards of international behaviour that we would expect."

Greste writes that the trio's freedom depends on continued pressure being placed on Egyptian authorities.

"Our freedom, and more importantly the freedom of the press here, will not come without loud sustained pressure from human rights and civil society groups, individuals and governments who understand that Egypt stability depends as much as on its ability to hold open honest conversations among its people and the world, as it does on its ability to crush violence," he said.

"We know it is already happening, and all of us are both moved and strengthened by the extraordinary support we have already had, but it needs to continue."

Read Greste's letter in full: