The Justice and Development Party, which accepts the country's monarchy, said it would capture more than 100 of 395 seats in Parliament, The Daily Telegraph of Britain reported.
Official results are expected Sunday.
The provisional Interior Ministry said turnout was 45 percent, up from 37 percent in the last parliamentary election in 2007, and analysts said the high turnout would add credibility to constitutional reforms.
"We have already won over 80 seats and I can tell you that we will easily have over 100 seats. This is a historic turning point," said Mustapha el Khelfi, the managing editor of Attajdid, which supports the party, known by its French initials PJD.
After huge pro-reform protests this year, King Mohammed VI cut back on his powers, which had been nearly absolute.
Under a constitution approved by a wide margin in a July referendum, the monarch must now pick the country's prime minister from the party with the most seats in Parliament, instead of choosing anyone he wants.
PJD has focused on issues including high unemployment, raising the minimum wage, reducing poverty and fighting corruption.
About 13.5 million Moroccans were eligible to vote.