Alluni, who gave his testimony to the Spanish court on Monday, also described how he had interviewed Osama bin Laden weeks after the 11 September 2001 attacks.
Alluni, who appeared calm and relaxed before the three-judge panel, described how he was taken blindfolded by armed men to meet bin Laden shortly after the attacks in New York and Washington.
"I was taken out of the car, they removed the blindfold and there was bin Laden. He welcomed me and said that he was sorry for the inconvenience," Alluni said.
Alluni is accused by the Spanish investigative magistrate Baltasar Garzon of forming a radical Muslim indoctrination unit in the 1990s while living in the southern Spanish city of Granada.
He is also accused of being the right-hand man of the alleged leader of the Spanish cell, Syrian-born Spaniard Imad al-Din Yarkas, who is also on trial.
Alluni denied that he had close relations with Yarkas, whom he said he met in the early 1990s.
"We met just as Syrian nationals. I've always thought that he was a nice and polite man," Alluni told the court.
"This relationship was never intense or continuous."
Spainish judge Baltasar Garzon
has been investigating Alluni
Alluni added he had no knowledge of Yarkas recruiting men for alleged terrorism training camps in Afghanistan and elsewhere, as claimed by Spanish prosecutors.
Alluni was initially released owing to a heart condition a month after his September 2003 arrest, but was re-arrested last November.
In March, he was again released from preventive detention, but on condition he be placed under surveillance.
Alluni is accused of having connections with Yarkas, transferring money to Afghanistan during his professional trips there, making use of his journalistic activities to finance, support and organise al-Qaida activities, and being a member of al-Qaida's Spanish cell.
A special committee of observers, including those of Arab and international rights organisations and the head of Reporters Sans Frontiers, were present at the hearing.
The court is expected to finish the hearings within two months.