Abdel Aziz, who allied himself with the West in the so-called war against terrorism in West Africa, was sure to win the poll amid opposition’s boycott.
The opposition has boycotted the polls, calling the election a grotesque theater with victory guaranteed for Abdel Aziz who has control over state institutions.
According to reports, voter turnout has been low in wealthy areas in the capital, but Aziz strongholds on the outskirts of Nouakchott were witnessing crowded lines at the polling stations.
A runoff is slated for July 5 in case no candidate wins an outright majority.
The opposition also boycotted last year's parliamentary elections – describing the organisers as biased and the process flawed.
Talks to try to persuade them to take part in Saturday's vote broke down in April and that left Abdel Aziz with no major rivals.
"Anyone can see that these [opposition] parties are void of any content and no longer even have a political role to play, reflecting the level of their leaders," Abdel Aziz told reporters after voting. He is a former head of the presidential guard.
Voting was scheduled to end at 7 pm local time and ballot counting began immediately after.
An unnamed elections observer with the Arab Parliament said he had not heard of any reports of serious incidents during the vote.
"We have remarked that the operation is taking place in total calm and all the means have been put in place for the proper execution of the election," he said.
As many as 1.3 million people were eligible to vote in the elections with just a handful of candidates to choose from.
Mauritania has reserves of iron ore, copper and gold and is trying to boost investor interest in its oil and gas.
However, it has long been plagued by political instability and military coups.