The trials come amid growing efforts by the governments of Algeria, Mauritania, Mali and Niger to counter a wave of recent desert kidnappings of foreigners claimed by Al-Qaeda in the Islamic Maghreb, or AQIM.
The three men -- Sidi Ould Sidna, Mohamed Ould Chabarnou, and Maarouf Ould Haiba -- are accused of having shot five French tourists in the town of Aleg in December 2007, leaving four dead and one seriously injured.
Nine other suspects are being tried in the Aleg case for their complicity. Six other trials for other incidents are scheduled for the remaining AQIM suspects.
Lawyers for Chabarnou and Haiba said their clients would plead not guilty, and Haiba's lawyer said his client's confession was obtained illegally.
"I will first tackle the flaws of the record, as, among other things, the confessions contained in the minutes were obtained through torture," lawyer Maitre Zaim told Reuters before the trial.
Mauritanian officials were not immediately available to comment.
Isselmou Ould Mustafa, editor of the local newspaper Tahalil Journal, said security sources in Mauritania believed the three men were associated with AQIM leader Mokhtar Belmokhtar, and had been trying to boost their credibility within the group with a high profile attack.
Sidna and Chabarnou were arrested in Guinea Bissau in January 2008, while Haiba was arrested shortly afterward in Nouakchott.
AQIM grew out of the Salafist movement in Algeria, and has shifted south into the Sahel region in recent years where it is taking advantage of the vast and lawless desert to pursue its operations.
Security analysts believe the group is becoming less ideological and more opportunistic, raising funds by ransoming hostages and getting involved in drug trafficking.
AQIM currently claims to hold two Spaniards and a Frenchman hostage, all taken remote parts of the Sahel region.