"The Union for the Republic is the leading political party according to provisional results" of the first-round September 1 vote, commission spokesman Mustafa Sidel Moktar told AFP.
The party has so far won 67 of the 157 national assembly seats, compared to 14 for the second-place Islamist party Tawassoul, as well as four of the 13 regional councils and 108 of 219 municipalities, he said.
The turnout was 73.4 percent, Mohamed Vall Ould Bella of the Independent National Electoral Commission (CENI) said on Saturday, in a country with a registered electorate of some 1.4 million, Presstv Reported.
A second round vote will be held on September 15 to decide 22 national assembly seats, nine regional councils and 115 municipalities.
The elections in Mauritania, a frontline state in the fight against extremists, were seen as a test for head of state Mohamed Ould Abdel Aziz seven months before a presidential vote.
The opposition boycotted the last polls in 2013 but a record 98 parties took part this time. Aziz, 61, who came to power in a coup in 2008, won elections in 2009 and again in 2014 for a second five-year term.
He has been frequently accused by opposition figures and NGOs of rights abuses, and though he says he will not seek a third mandate -- which would be against the constitution -- statements by ministers and supporters have led some to suggest he might.