Zainab Tariq Aziz said her sister, mother and aunt were allowed to see Aziz for the first time more than two years after he was imprisoned by US forces.
She said her father did nothing wrong during his years in the former Iraqi government.
"He was tired, he had lost a couple of kilos, but he was in good spirits and felt relief when he saw us," she said.
She said the family had driven from Amman, capital of neighbouring Jordan, for the half-hour visit. "Although we did not see my father for two years, they only gave us 30 minutes to meet him and in the presence of two Arabic speaking US soldiers," she said.
She said her father, who was also a former foreign minister, asked about other members of the family and seemed anxious for news about what was going on elsewhere in Iraq.
"He asked us about what was going on in the outside world, and also what was the latest news about the constitution," she said.
Negotiations are underway to draft a new constitution by a Monday night deadline.
She said Aziz met with the family in a wooden trailer divided by a glass partition. One American soldier stood behind the partition and the other was inside the part where they met with Aziz, she said.
"They did not even allow us to show him his grandchildren's pictures or letters," Zainab said. "He was worried about us and how we were doing and kept asking about his grandsons and how are they doing in schools."
Aziz tried to comfort the family by telling them he is not afraid of standing trial. She quoted him as saying: "I did not hurt anybody and my page is clean. So I am not anxious about the trial".
Aziz has not been formally charged with any offence but is under investigation for his role in Saddam Hussein's government.