Aljazeera spokesman Jihad Ballout criticised Spain’s detention of Alluni, saying it “is another inconvenience to which journalists in general and those from Aljazeera in particular fall victim”.
Ballout added that Aljazeera had appointed a lawyer for Alluni and had been in contact with Spanish authorities as well as non-governmental organisations defending the freedom of the press.
Soon after his arrest an Arab rights body called for his release.
The Arab Commission for Human Rights told Aljazeera the Spanish action was a serious attack on press freedom.
It said the arrest dishonoured Spain and the police should apologise immediately to Alluni and his family.
Alluni, who rose to prominence during the Afghanistan and Iraq wars, is of Syrian origin but is a Spanish citizen.
He narrowly escaped death when US warplanes bombed the Kabul offices of Aljazeera during the closing days of the war to oust the Taliban in November 2001.
“Do you think he would put himself in the wolf’s mouth if he had to hide from anyone?”
Fatima al-Zahra, Alluni’s wife
Alluni, one of the channel’s highest-profile journalists, was arrested at 2pm (1200 GMT) while on holiday near the southern Spanish city of Granada.
His wife, Fatima, told Aljazeera that police arrived at their Alfacar home with a warrant for his arrest.
“Police in civilian clothes came to our door with a warrant to search the house and to arrest Taysir because they said he was a member of al-Qaida,” she said.
Police then took Alluni to Madrid after accusing him of using his profession to enter into contact with “terrorists”.
She strongly denied the allegations against her husband.
“Do you think he would put himself in the wolf’s mouth if he had to hide from anyone?” she asked.
Police have accused Alluni of having connections with Imad Eddin Barakat Yarkas, alias Abu Dahdah, who was arrested on suspicion of being the ringleader of an Islamist cell which Spanish authorities dismantled in November 2001.
Spanish intelligence sources told Aljazeera that Alluni was being held under anti-terrorist legislation.
The laws allow police to detain suspects for three days without access to lawyers or family.
They said he was arrested on the orders of Spanish Judge Baltasar Garzon, best known for an unsuccessful attempt to put former Chilean dictator Augusto Pinochet on trial.
Garzon and Spanish state prosecutor Pedro Rubira suspect Alluni of involvement in “the organisation of, support for and infrastructure of this cell”, according to the warrant for his arrest.
Alluni also stands suspected of “furnishing al-Qaida with funds
in Afghanistan”, where he was an Aljazeera correspondent during the 2001 US-led war which brought the end of Taliban rule.
It is thought the police want to try him before a special tribunal which specialises in cases of terrorism and organised crime.
Alluni was one of Aljazeera’s eight correspondents in Iraq and was expelled by Iraqi authorities during the war.
Before that he worked as a translator during the 1990s for Spain’s EFE news agency.
Spanish authorities have tracked his movements since at least October 2001, when the newspaper El Pais reported that Alluni’s phone had been tapped by the authorities while he was working for the agency’s Arabic section.
He later moved with his family to Afghanistan and stayed there until the Taliban were overthrown by the Americans in 2001.
He had been trying to set up an Aljazeera office in Madrid.