Deposed Libyan leader Muammar Gaddafi's former prime minister al-Baghdadi al-Mahmoudi extradited from Tunis on June 24 Mr Mahmoudi was transferred to jail after being taken back to Libya by helicopter.
Mr Mahmoudi, 70, had fled to Tunisia during the uprising against Col Muammar Gaddafi last year.
Mr Marzouki's office said in a statement that the decision to extradite Mr Mahmoudi was taken without consultation and without his agreement.
Mr Mahmoudi is the first senior Libyan official to be returned for trial.
Mr Marzouki had promised earlier this year to hand over Mr Mahmoudi if he were guaranteed a fair trial in Libya, but in May he said he was in principle opposed to the move.
Human rights groups had asked Tunisia not to extradite him, saying he could be subject to human rights violations in Libya.
A Tunisian government statement said the extradition did not require the president's signature.
It said the decision to extradite had been made following a report by a Tunisian delegation to Tripoli, which found that the conditions for a fair judicial process had been met.