Mohamed Ould Biya, a spokesman for the four opposition candidates, said electoral lists had been tampered with and voters had used fake ballot papers and identity cards during the poll to add to Abdel Aziz's tally.
But interior minister Rzeizim said there had been no formal complaints and an African Union team in the country called the elections transparent.
Neither the United Nations nor the European Union, which cut aid to Mauritania as a result of Abdel Aziz's coup in August last year, sent election observers to Mauritania.
The result must still be confirmed by Mauritania's constitutional court.
Abdel Aziz's opponents in the election included: Ahmed Ould Daddah, a veteran opposition figure; Ely Ould Mohamed Vall, another former coup leader; and Messaoud Ould Boulkheir, a politician who has spearheaded the challenge to last year's coup.
Messaoud and Ould Daddah were Abdel Aziz's closest challengers with 16.3 and 13.7 per cent of the vote, respectively, according to the interior ministry figures.
As president-elect, Abdel Aziz vowed to beef up Mauritanias army and "fight terrorism in all its forms".
"We will fight terrorism in all its forms, we will fight it ... by strengthening the resources at the army's disposal," he said in his first address since being declared the north African country's new leader.
The former general's words come just weeks after an American teacher was shot dead in the capital Nouakchott, with a branch of al-Qaeda claiming responsibility.
Ahead of the elections, Mauritanian police clashed with suspected al-Qaeda fighters in the capital.
The US had supported Mauritania's offensive against fighters in the country, but froze co-operation after last year's coup.