The manual recount was demanded by the supreme court in polling stations with contested results, in line with a decision by the outgoing parliament following allegations of fraud.
Parliament's deputy speaker Aram Sheikh Mohammed announced "the end of the third parliamentary mandate", at a gathering attended by 127 members of the 328-seat house.
Since the aftermath of the 2003 US-led invasion that toppled dictator Saddam Hussein, Iraq has had three parliaments each with a mandate of four years.
The last ballot was won by populist cleric Moqtada Sadr's electoral alliance with communists, as long-time political figures were pushed out by voters seeking change in a country mired in conflict and corruption.
Results of the May election were contested mainly by the political old guard.
The supreme court has ratified a decision by the outgoing parliament to dismiss Iraq's nine-member electoral commission and have them replaced by judges.
The judges' spokesperson, Laith Hamza, said Saturday that the partial recount would start Tuesday in the Kurdish provinces of Arbil, Sulaymaniyah and Dohuk, as well as in Kirkuk, Nineveh, Salaheddin and Anbar.
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