Commission official Aziz al-Kheikani said the distribution began in four new provinces including the capital Baghdad today in preparation for the April 30 ballot.
Voters in 13 of Iraq's 18 provinces began to receive cards, which contain a computer chip, three weeks ago.
He said authorities will decide "soon" on when and how to distribute the cards in the remaining province, Anbar.
An al-Qaida offshoot and other insurgent groups have taken control of the city of Fallujah and parts of the provincial capital, Ramadi.
Thousands of families have left and government offices have shut down.
The clashes in Anbar have contributed to a spike in violence. Last year was Iraq's bloodiest since the worst of the country's sectarian bloodletting began to subside in 2008, with 8,868 killed, according to the UN.
In the latest attacks, militants set off three explosives-laden cars parked near four houses of local security and civilian officials in the city of Tikrit, killing at least five people included two policemen, a police officer said.
A medical official confirmed the casualty figures. Both officials spoke on condition of anonymity as they were not authorised to release information.
Nearly 22 million Iraqis are eligible to cast their ballots in parliamentary election, scheduled for April 30, to choose 325 lawmakers.
The voting is the third since 2006.
