"No, I will not sign this kind of order because I am a socialist," Talabani, a Kurd, told France 24 television during an interview.
"I feel for Tareq Aziz, because he's an Iraqi Christian, and he's also an elderly person over 70 years old. That's why I will never sign this execution order."
Aziz was given the death penalty on October 26 for a crackdown on religious parties in the 1980s, and is also on trial for a crackdown on Iraqi Kurds.
Talabani has previously said that he is generally against capital punishment, and declined to confirm some court execution orders but without preventing the hangings going ahead. Aziz was the latest member of Saddam Hussein's fallen regime to be ordered to die, but Talabani said it was time to turn the page on the punishment, barring for some sectarian crimes.
"I think that the page of executions needs to be turned, except concerning the crimes committed at the cathedral of Our Lady of Perpetual Help and crimes against Shiite pilgrims and holy sites," he said.
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