Former Sunni speaker secured 182 votes in the 329-seat legislature with significant support from Shia political blocs.
Ongoing disputes between the major parties – KDP and PUK – could complicate the formation of a new government.
Turkey says it hit targets linked to the Kurdistan Workers’ Party, which it blames for the attack on TUSAS.
More than 1,000 candidates, including 368 women, are vying for election to the 100-seat regional parliament.