Tantawi's comments were made on Sunday at a ceremony south of Cairo, and come a week after he testified at Mubarak's trial, which is under a total media blackout.
The Associated Press reported that leaks of Tantawi's testimony suggested he had sought to clear Mubarak of the charges he faces over the killing of nearly 850 protesters.
Tantawi, who served as defense minister under Mubarak for 20 years, was quoted as saying:
We were not asked to fire at the people and we will never use fire. My testimony in the case of the killings of the protesters was the testimony of a sincere man and a soldier of 40 years, one for God and Egypt ... We were not ordered to open fire at citizens and we will never do that.
The BBC says that Tantawi's testimony is seen as vital in the trial, in which Mubarak could face the death penalty if found guilty of complicity in the killings.
The network cited complaints from lawyers that Tantawi had left the courthouse early, without allowing himself to be cross-examined.
He had initially been due to testify earlier in September, but failed to show up. Media reports said Tantawi had blamed his busy schedule, and had offered to submit a written testimony.
Along with about two dozen other generals, Tantawi sits on the ruling Supreme Council of the Armed Forces (SCAF), which took control of Egypt following the toppling of Mubarak.
Although SCAF has promised to return to the country to civilian rule after a transition period, protesters say its use of emergency law reverts to the same tactics used by Mubarak to stifle dissent.
In other news on Sunday, political parties in Egypt pulled back from threats to boycott Egypt's elections, slated for November 28, instead accepting concessions offered by the military.
The parties will now be allowed to field candidates for seats that had previously been allocated to independents.