According to preliminary results, the New Azerbaijan party has won 64 of 124 seats in parliament, the Russian news agency RIA Novosti reported.
However, opposition parties have challenged the results, complaining of widespread irregularities. Ali Kerimli, the chairman of the Popular Front Party, said the voting was "clearly falsified," the Pravda.ru Web site reported.
Kerimli said "peaceful, constitutional resistance to this falsification" would start Tuesday.
A spokesman for the election commission said voter turnout was close to 47 percent, more than 2 million of the 4.6 million registered for the election.
Sunday's elections -- the first since Ilham Aliyev replaced his father, Heydar Aliyev, as president in 2003 -- are seen as an important test for democracy in the oil-rich former Soviet republic, the BBC reported.
Hundreds of international observers monitored the voting, and the U.S. government sponsored one exit poll as a check on the official count.