Fatullayev, winner of last year's Amnesty International Media Award for Journalism Under Threat, is currently serving an eight-and-half-year sentence, on charges of defamation and terrorism.
Amnesty International reports that Fatullayev's father, Emin Fatullayev, has received death threats after publicly speaking out on behalf on his son.
The European Court of Human Rights (ECtHR) ruled in April that he had been wrongfully imprisoned and should be released. But he remains in prison - and has since been charged by the Azerbaijani authorities for the possession of illegal drugs.
At this week's Amnesty Awards, special mention was given to Fatullayev's plight. "The continuing imprisonment and persecution of Eynulla Fatullayev brings shame on Azerbaijan," said Amnesty International UK director Kate Allen.
"It's amazing that the authorities are so scared of the words of one journalist that they would damage their international standing in this way, even questioning the authority of the European Court of Human Rights."
Today [Thursday] at midday, campaigners are due to gather outside the Azerbaijan embassy in London and give a letter to the ambassador signed by authors including Monica Ali, Alan Ayckbourn, William Boyd and Philip Pullman.
"The persecution of journalists such as Eynulla Fatullayev is commonplace in Azerbaijan," said John Kampfner, chief executive of Index on Censorship.
"The authorities have curtailed freedom of expression and have shown persistent hostility towards independent and opposition media. Journalists continue to be harassed, threatened, attacked and imprisoned for conducting their professional activities. Defamation and false charges are increasingly used to silence critical voices."
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