Aziz and two other members of the former regime of Saddam Hussein were sentenced to death in October for their roles in the persecution of Shiites in the 1980s. The sentence sparked international calls for leniency, though Washington said the matter was an Iraqi affair.
Talabani, a Kurd whose ethnic community endured gas attacks launched by the Baathist regime of Saddam Hussein, told France 24 in a Wednesday interview he wouldn't sign off on the Aziz death sentence.
"I will sign no death sentence at all because as a social democrat, I'm against the death penalty," he said in Paris.
Leaders from the Vatican, Moscow and Greece have called on the Iraqi courts to call off the hanging of Aziz, who was the only Christian member of Saddam's regime.
The former minister, who suffered a stroke in January, has less than 30 days to appeal his sentence, though family members said he is resigned to his fate.
Talabani made similar pleas in 2007 when he called for a delay in the execution of two of Saddam's former henchmen for their role in a 1980's massacre of Shiites.
The BBC reported at the time that Talabani has a reputation for opposing the death penalty but that, as president, he has no power to annul or delay an execution order.