The tribunal is stepping up the process of questioning former government loyalists about war crimes, officials say.
The tribunal released film showing Aziz, looking relaxed in a white prison robe, responding to questions about an exchange of letters he had with Saddam's office over a written question from the United Nations about the killing of Kurds in 1991.
"I had no authority then," Aziz told the prosecutor, explaining why he had not provided the statistics requested.
Several other officials were also questioned, including Saddam's cousin, Ali Hassan al-Majid, who appeared before a judge for the second time in two weeks.
In the tribunal footage, Majid, who wore a traditional Arab head-dress and look old and tired, examined documents shown to him by the court.
Two of Saddam's half-brothers, Watban and Barzan al-Hassan, were among six other officials questioned last week, the tribunal said in an earlier statement.
The Iraqi government wants to put Saddam and other officials on trial as soon as possible. Saddam was questioned two weeks ago. Officials with the tribunal, set up 18 months ago, say the process cannot be rushed and no trial date has been set.
It was not clear when Aziz was questioned, but his lawyer Badea Aref, who was present during the questioning, said that it happened on June 21.
"The prosecutor was impolite to Mr Aziz and he even told him: 'You are a criminal'. This angered Mr Aziz and me, and we had heated argument with him," he said.
"The prosecutor was impolite to Mr Aziz and he even told him: 'You are a criminal'"
Tariq Aziz's lawyer Badea Aref
"It is not acceptable and I am filing a complaint asking for the prosecutor to respect the defendant.”
Aziz, a rare Christian among the top Baath party leadership and often considered number two in the leadership, is alleged to have been involved in several party purges in the 1970s and 80s during which an unspecified number of people died.
A fluent English speaker, he was the face of Saddam's government in foreign capitals and at the United Nations.
Majid was questioned with two other officials about using chemical weapons in 1988 and dropping poison gas on Kurdish villagers in a military operation called Anfal.
Also questioned on the same accusations two weeks ago were Taha Yassin Ramadan, Saddam's former vice-president, and Saadoun Shaker, interior minister early in Saddam's rule, who was also asked about the killing of Shia villagers in 1982.
The killings in Dujail - more than 140 villagers were killed after a failed assassination attempt on Saddam as his motorcade passed through the village - may be key to an early trial of Saddam, who was questioned about the incident himself.