Ricardo Miguel Cavallo is wanted in Spain on charges of genocide and torture.
He was arrested last week while trying to board a plane to leave Mexico for Argentina, where he would not face prosecution, thanks for an amnesty for the military during the period of the 1976-83 dictatorship.
"The government of Argentina insists on the principle of territoriality in the application of criminal law," Mr de la Rua said.
The principle says that a person can not be tried in a foreign country for crimes committed at home.
There has been no official response from Mexico over the issue.
The application for extradition comes from the Spanish judge, Baltazar Garzon, who faced a similar challenge in his efforts to extradite the former military leader of Chile, Augusto Pinochet, from the United Kingdom.
Charges
Mr Garzon has been investigating Mr Cavallo for his role in Argentina's Navy School of Mechanics, a notorious detention camp and torture centre for political prisoners during the military dictatorship.
The judge has been hearing testimonies from victims of military repression who say Mr Cavallo was one of their torturers at a detention centre in Buenos Aires.
Human rights groups estimate that about 30,000 people were killed, or abducted during military rule in Argentina.
Mr Cavallo has denied his involvement and says he is the victim of mistaken identity and that he played no part in Argentina's "Dirty War".
Mr Cavallo is charged in a 196-page document with the torture, disappearance, and execution of 21 people.
He is also linked to 227 disappearances and 110 cases of torture, as well as the alleged kidnapping of 16 babies born to women held at a notorious detention centre.
"It is clear that [Cavallo] participated in the whole system of repression, disappearance and elimination of persons," said Judge Garzon.
The judge said he did not originally indict Mr Cavallo along with another 98 Argentine officers because there was confusion over his real name.
He apparently called himself Miguel Angel Cavallo while working for the military regime.