But Saad Eddine Othmani, the party's leader, who was expected to win in a constituency in Casablanca, was less confident.
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"We are certain to have at least 40 seats but we are having trouble in counting up exactly because the authorities don't give out all the figures," he told AFP news agency.
"The results are too incomplete to be able to say whether or not we will be the biggest party," he said.
Even if the PJD does still become the largest single party after the election, the king is not expected to choose a prime minister from the party.
During the campaign Daoudi had predicted the PJD would get 80 seats against 42 in the outgoing parliament, while Othmani had forecast 70.
Official results were expected on Sunday.Low turnout
Chakib Benmoussa, the interior minister, said the 41 per cent turnout on Friday was "the lowest in the history of the kingdom".
"There are no chances of Islamic groups winning as most people in Morocco are enjoying its liberal culture"
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He admitted the turnout was disappointing.
"The challenge today is to think of the best way of mobilising the electorate in support of political action. That is everybody's responsiblity: officials, political parties and civil society," he said.
International observers, scrutinising a Moroccan election for the first time, were due to report their preliminary findings late on Saturday.
Analysts had predicted that the PJD had a chance of winning cabinet seats if it emerged as the single biggest party.
The party is particularly popular among the poor in many of the country's marginalised communities.
In 2002, it won 42 seats 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 against violent Islamist groups.
Thirty-three political parties and dozens of independent candidates were seeking seats in the kingdom's 325-member assembly.