The PJD, which has vowed to tackle corruption, could become the largest single party after the election, although the king is not expected to choose a prime minister from the party.
The first partial results were due to be announced on Saturday whilst official results were expected on Sunday.
Lauren Taylor, reporting for Al Jazeera from Tangiers, said that at one polling station, where 700 people were registered to vote, only 155 people cast their ballots.
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She said the low turnout across the country "is likely to favour the PJD because their roots are slightly better organised, they have an efficient system at getting out the vote".
"But keep in mind that ... even if they are the biggest party in government, they will need a coalition party to help them govern. That's the way the [proportional representation] system works."
International observers, scrutinising a Moroccan election for the first time, were due to report their preliminary findings late on Saturday.
Saad Eddine Othmani, the secretary general of the party predicted that they would win at least one million of the 15.5 million eligible votes and at least 70 seats in the 325-deputy chamber.
"Morocco, like any Muslim state, has to choose Islam," sadi Ali Sunari, an engineer, as he voted in the capital Rabat.
"All other parties have achieved nothing for us."
"There are no chances of Islamic groups winning as most people in Morocco are enjoying its liberal culture"
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Analysts say the PJD has a chance of winning cabinet seats if it emerges as the single biggest party.
The party is particularly popular among the poor in many of the country's marginalised communities.
The PJD won 42 seats in 2002 but was kept out of the five-party governing coalition led by Driss Jettou, then a non-politician appointed by the king.
It includes the Union of Socialist Popular Forces (USFP), which is seen as the individual party most likely to challenge the PJD for the highest number of seats, and the nationalist Istiqlal party.
A complex voting system will make it almost impossible for any group to win a majority.
Some fear the PJD wants Islamic rule, but the party calls al-Qaeda an "enemy", and some in the establishment see the PJD's moderation as taking a stand violent Islamist groups.