The father, brother and wife of Islam Salih had earlier asked for visiting permission, but their request was denied after the authorities demanded a written request.
Salih's family remain in the dark over his whereabouts.
Salih, Aljazeera's bureau chief in Khartoum, was arrested last Thursday and his offices closed.
The arrest came a day after security forces raided the bureau and took Salih for questioning.
Prior to his detention, Salih had received threats from the security forces over Aljazeera's political coverage of Sudan.
Aljazeera's spokesperson Jihad Ballout voiced his anger over Salih's current situation.
"It is an outrageous state of affairs when a journalist in this day and age is afforded a treatment that ought to be reserved to criminals," said Ballout.
"At the end of the day, Islam Salih was only doing a job in a professional way and reflecting on aspects that are newsworthy to the Sudanese people and Aljazeera's audience at large, adhering to our professional value of the opinion and the other opinion."
"We agree with the overwhelming consensus amongst the media community exemplified by the Arab Human Rights Committee that our colleague Islam Salih should be released immediately," pointed out Ballout.
In a statement made available to Aljazeera, the Arab Human Rights Committee has condemned Salih's arrest, and called for his immediate release.
The committee also called for "an end all aggressive measures against journalists and reporters, and particularly against Aljazeera Satellite Channel."
Aljazeera's motto is 'the opinion
and the other opinion'
Paris-based media rights group, Reporters Without Borders, condemned the detention.
"We call on the security services to authorise the immediate reopening of Aljazeera's bureau in Khartoum and to stop censoring this TV network," said the secretary general of Reporters Without Borders, Robert Menard, on Friday.
"The confiscation was clearly motivated by displeasure with Aljazeera's coverage of Sudan," the media rights group said.
Widely watched in the Arab world, Aljazeera has upset many conservative Arab governments with its reporting.
Human rights organisations have often condemned Sudan for cracking down on freedom of expression.
In its 2003 report on Sudan, Amnesty International said security forces continued to limit media freedoms.
Amnesty added that authorities unlawfully arrested journalists and editors and fined or suspended newspapers. Sanctions were also imposed for publishing articles critical of the government.
Last month, the daily, al-Ayam, was forced to suspend publication after it was accused of harming Sudanese national interests and helping its enemies.