Election seen as a test of the commitment to democracy in the former Soviet state.
The announcement of the results will be followed within hours by initial findings from voting monitors from the Organisation for Security and Co-operation in Europe (OSCE).
Nazarbayev, 67, in power since Soviet times in 1989, has overseen rapid economic growth in the oil-rich Central Asian state.
However, his electoral victories have never been judged free and fair by international poll monitors.
Saturday’s poll for the lower house of parliament, the Mazhilis, set Nazarbayev’s wish to keep a tight grip on the vast country against his desire to be viewed in the West as a reforming international statesman.
The ANSDP said it had gathered photographic evidence of a range of violations, including multiple voting and campaign literature for Nur Otan in polling stations.
Nazarbayev wants Kazakhstan to chair the OSCE, a 56-member democracy, rights and security body, in 2009 but has faced opposition due to his poor record on democracy.
He called the election two years early after enacting constitutional changes that hand the lower house more powers such as naming the prime minister.
They also removed any limit on how many terms he can serve as president.