The election, which was delayed for a month in order to end an opposition boycott, is being seen as a bid to signal to donors and investors that the country is ready to take its place internationally.
Price cuts pledged
Mohamed Ould Abdel Aziz, the former general who instigated last year's coup and who appears the favourite to win, cast his ballot in the capital, Nouakchott.
He has promised cuts in food and fuel prices that are likely to endear him to Mauritanians, 40 per cent of whom live under the poverty line.
Abdel Aziz resigned from the army and the military administration in April so that he could run in the elections as a civilian.
He toppled Sidi Ould Cheikh Abdallahi, Mauritania's former president, in August 2008, provoking international criticism.
Eight other candidates are contesting the election, including Ely Ould Mohamed Vall, who mounted a popular coup in 2005, ousting Mauritania's long-standing military ruler, and Ahmed Ould Daddah, a civilian opposition figure.
"This election represents the most important challenge ... where our country chooses to either come out of ... a very grave crisis and extremely dangerous for our country, or it chooses to remain in this crisis," Vall said.
Kissy Agyeman-Togobo, an analyst with Global Insight, said: "The most likely scenario is for [Abdel] Aziz to become leader, but this time through the ballot box."
Abdel Aziz vowed he would win enough support to avoid a runoff, and "bring change, development and prosperity" to Mauritania.
But if no candidate wins the 50 per cent majority needed to avoid a runoff, a second round will be held on August 1.
Shortly before polls opened on Saturday morning, two men were arrested after police exchanged fire with armed men in Nouakchott.
The incident occurred in the same neighbourhood where an American teacher was shot dead last June.
The fatal shooting was claimed by al-Qaeda in the Islamic Maghreb, which said the American was trying to convert Muslims to Christianity.
Abdel Aziz made cracking down on al-Qaeda a cornerstone of his justification for seizing power, accusing Abdallahi of slackening off on the group.