Addressing the Mauritanian people, through an interview with Al Jazeera, Vall said: "I tell them that they are in front of a historic opportunity which is rare in their country and in all the countries in the area where they are.
"Therefore, I tell them 'do not waste it'".
A military government deposed Maaouiya Ould Taya, the Saharan country's long-time military leader, in a coup in August 2005 and pledged to usher in democratic reforms aimed at return to civilian rule.
After a constitutional referendum in June, Sunday's local and parliamentary poll comes ahead of planned senatorial elections in January, followed by presidential election in March 2007.
Vall, the country's military leader, has said he would not stand in any future presidential elections.
"I will not run [for presidential elections]. I will respect what I have said and will do what I have said," he confirmed.
He said the elections would be "honest and transparent" and carried out under the supervision of the African Union (AU), the European Union (EU), the Arab League and some US organisations.
Mohamed Ould Moloud, president of the Union of Forces of Progress and the current rotating head of the opposition Forces of Change for Democracy Coalition, said: "There are positive indications on the neutrality of the administration.
"If this is confirmed on the day of the vote, it will be a success for our democratic experience."
Frank-Walter Steinmeier, the German foreign minister, visited the Mauritanian capital, Noukachott, on Saturday.
Steinmeier said Mauritania had begun a democratisation process "under the most difficult conditions" and that he hoped to find areas where Europe and Mauritania could work together to further modernise the country.
The Independent Electoral Commission said that "all was in place" in the 2,336 voting booths scattered across the western African country and hailed a campaign that wound up on Friday without any major incident.
Results are to be announced on Tuesday, with a second round of legislative voting scheduled for December 3.