The UK-based group has called on Spanish authorities to allow its lawyers to visit Alluni in his prison cell, after his re-arrest last week.
A Spanish court upheld his indictment on charges of allegedly belonging to an al-Qaida-linked group, officials say.
In a statement, the AOHR said it wants to ensure that Alluni is receiving the correct legal advice. The group said Alluni’s detention should be seen in the context of the “campaign targeting Aljazeera”.
An affiliation of Pakistani cameramen and producers has also issued a statement condemning the arrest of Alluni. The union said his arrest was an attack on freedom of the press.
At the same time, an independent union of Moroccan public sector practitioners has also appealed to the Spanish prime minister to allow them to send a medical team to check Alluni’s health condition.
Alluni, in his 50s, was first arrested on 5 September 2003 in Grenada, where he lives with his family.
He is one of 41 people – including al-Qaida leader Usama bin Ladin – charged with links to, or membership of, the network and of using visits to Kabul to forge links with al-Qaida.
Alluni is famed for his coverage
Suffering from a heart defect, he was released on bail in October 2003 but told he was not allowed to leave the country.
The decision to detain Alluni, a Spaniard of Syrian origin, was taken after a request by the Spanish prosecutor’s office, which said there was a strong risk that he would try to flee the country before his trial.
Alluni found fame with exclusive reporting from Afghanistan during the US-led war on the Taliban launched in October 2001, interviewing Bin Ladin and later reporting from Baghdad on the war in Iraq.
Aljazeera spokesperson, Jihad Ballout, said Alluni’s arrest came as “no surprise”.
“We are convinced that Alluni did no more or no less than pursue his job in a professional manner,” he said.
“We have faith in the integrity of the Spanish legal system which we trust will ultimately acquit him of all charges.”
The trial has been set for February 2005.