Abderrazak Makri, who heads the Movement for the Society of Peace (MSP), said his party and its ally the Front for Change would have won if there had not been any fraud.
President Abdelaziz Bouteflika's National Liberation Front (FLN) and its ally the Rally for National Democracy (RND) won a clear majority in Thursday's elections.
"The administration allowed the thugs of the FLN and the RND to stuff ballot boxes and commit violence without it intervening," said Makri, whose party has links to the Muslim Brotherhood.
Islamist parties won 67 seats in the polls, up from a total of 60 in the 2012 elections.
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Makri said 70 per cent of polling stations did not have any observers due to a misinterpretation of the electoral law.
According to the Islamist leader, in several areas, the vote count of which the MSP obtained a copy does not coincide with the final vote count that was announced.
Makri said abstention in the country would diminish considerably when elections become clean, after a turnout of 37 per cent in Thursday's vote.
But Makri said he would not encourage Islamist lawmakers to resign from parliament, and instead press for change within public institutions.
Thursday's vote was marred by voter disillusionment over what many see as broken government promises and a political system tainted by corruption.