The vote on Friday was to choose about 23,000 town and local district councillors in the North African country's first municipal elections since reform-minded King Muhammad, 40, came to the throne in 1999.
The Islamists of the Justice and Development Party (PJD) have been kept under close watch since suicide attacks by radicals in Casablanca in May shook the Muslim kingdom.
Early results on Saturday, mainly from rural areas, showed the two leading traditional parties, the Socialist Union of Popular Forces (USFP) and the conservative Istiqlal (Independence), taking most seats.
Results for about 30% of the seats up for grabs gave USFP and Istiqlal both 16% of the vote mainly in communes with less than 25,000 inhabitants.
The PJD trailed badly with only 1%, 87 seats out of a total of 6952 known so far, Interior Ministry figures showed.
These early results did not include large cities where a list voting system made counting slower. Final results there were not expected until Saturday night.
The showing of PJD candidates was closely watched as the polls were overshadowed by attacks in Casablanca on 16 May in which 12 Islamist bombers killed 33 people as well as themselves.
But under apparent government pressure and aware that public outrage over the attacks and a climate of fear made Islamists unpopular, the PJD consolidated and fielded candidates in only 20% of constituencies.
For the first time, Moroccans also elected city councils for the six largest cities, Casablanca, Fez, Marrakesh, Rabat, Sale and Tangiers.
At their Rabat HQ, Islamist party members ponder the poor results
There, the PJD presented candidates in 50% of constituencies and there also turnout was a low 37% of registered voters, according to official figures.
Deputy Secretary General Saad Eddine Othmani said the party did fairly well in Casablanca, in the eight of 16 constituencies it was present, and won the mid-sized central city of Meknes.
It was also leading in the number of votes in a dozen smaller cities such as Tetouan, Kenitra, Larache and Beni Mellal.
The authorities portrayed the elections, and last year's parliamentary ones which saw the PJD treble its number of seats, as fair and a big step towards real democracy.