Ahmed Ould Daddah, a top politician who heads the opposition Rally of Democratic Forces, said coup leader Ely Ould Mohamed Vall made the pledge during a meeting on Saturday with heads of more than 30 political parties in the capital, Nouakchott.
"There will be a referendum within a maximum one year, and immediately after that legislative elections," said Ahmed Ould Daddah.
"The military council does not have electoral ambitions, they will have no candidate in the elections," Messaoud Ould Boulkehir, the leader of another opposition party, said.
The military took power in a bloodless coup on Wednesday, ousting President Maaouya Ould Sid'Ahmed Taya as he was out of country.
Opposition parties have backed the coup but say they want to be involved in the decision-making process.
The aides who toppled Taya say
he ran a "totalitarian regime"
Taya, who had survived a series of coup attempts during his 21-year rule, was toppled by a group of army officers including some of his closest aides. They accused him of having ruled over a "totalitarian regime".
Taya had angered many Arabs in his homeland, which straddles black and Arab Africa, by establishing diplomatic ties with Israel and becoming a staunch US ally in West Africa.
He also turned Mauritania into one of the most repressive nations in the region towards Islamist movements, especially after narrowly surviving an attempted coup in 2003.
Scores of politicians and activists had been arrested since.
The United Nations, former colonial power France and the United States have all condemned the coup and the African Union has suspended Mauritania, demanding that Taya be restored to power.
But in the sand-blanketed capital Nouakchott, people took to the streets in jubilation, saying the putsch would usher in a new era of democracy in their country.