The ex-army general, who seized power in the northwest African nation in a August 2008 coup, has campaigned strongly on his success in fighting armed groups linked to Al-Qaeda at home and in neighbouring Sahel nations.
Small queues snaked outside several polling stations in the capital Nouakchott before voting got underway at 1230 IST.
Kidnappings and attacks by Al-Qaeda in the Islamic Maghreb (AQIM) were frequent when Abdel Aziz came to power, but he boasts he has turned his nation into a regional haven of peace thanks to his reorganisation of the military and security forces.
The mainly Muslim republic, sandwiched between the west coast of Africa and the Sahara desert, is seen by Western leaders as a bulwark against Al-Qaeda-linked groups.
In 2010 and 2011, Mauritanian troops carried out successful "preventative" raids on AQIM bases in neighbouring Mali, before the armed fundamentalists could carry out planned attacks on Mauritania.
But opposition critics argue that the price of peace has been authoritarian rule and have decided to boycott a vote that they regard as an "electoral sham" over the way it is being organised.
The ruling Union for the Republic (UPR) won a large majority in parliamentary and local elections last year, which were also boycotted by the opposition.
Abdel Aziz will face four challengers who have highlighted many of the country's sensitive issues such as complex race relations between black Mauritanians and the dominant Arabs.
The only candidate from the black African south is Ibrahima Moctar Sarr, who argues that non-Arab Mauritanians are "marginalised and victims of injustice".
Another contender is Biram Ould Dah Ould Abeid, who heads a movement to end slavery which, while officially abolished in 1981, persists as a deeply entrenched practice documented by rights groups.
While the country, which is nearly as big as Egypt, remains poor, it boasted a growth rate of of six per cent in 2013. Mauritania has produced oil since 2006 and is rich in iron ore as well as fish caught off its Atlantic coastline.
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