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 junta deposed the authoritarian government of the Saharan country’s long-time leader Maaouiya Ould Taya in a bloodless coup in August 2005 and pledged to usher in democratic reforms aimed at return to civilian rule.
After a landmark constitutional referendum in June, Sunday's local and parliamentary poll is a major milestone ahead of planned senatorial elections in January, followed by presidential election in March 2007.
Vall, the military leader, has confirmed that he would not stand in any presidential elections in the future.
|"I tell them that they are in front of a historic opportunity which is rare in their country"|
Ely Ould Mohammad Vall
"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.
Vall’s optimism was echoed by the Islamic republic's main opposition coalition and independent election organisers.
"There are positive indications on the neutrality of the administration," Mohamed Ould Moloud, the president of the Union of Forces of Progress and the current rotating head of the opposition Forces of Change for Democracy Coalition, said.
"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 in a show of support.
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 keep the country on that track.
Campaigning for the elections officially ended at midnight on Friday.
Results are to be announced on Tuesday, with a second round of legislative voting scheduled for December 3.
The Independent Electoral Commission, the first of its kind since independence, said that "all was in place" in the 2,336 voting booths scattered across the desolate, western African country and hailed a campaign that wound up Friday "without any major incident."