Initial reports indicated that dynamite was used to blow up the building, the interior ministry official said.
Nouri al-Maliki, the incumbent Iraqi prime minister, whose State of Law coalition is claiming credit for improved security since the peak of sectarian warfare in 2006-07, dismissed Sunday's attacks as "just noises to scare the Iraqi people from voting".
"But I know the Iraqi people. They have conviction. When there is a challenge, they persevere, and you will see for yourselves the large number of people that come out to vote."
Polling stations across the country were due to stay open until 5pm local time (1400 GMT) unless polling hours were extended.
However, the violence threatened to dampen voter enthusiasm. Twelve people were killed in a series of attacks in the Amil, Hurriya, Jihad and Khadraa districts of Baghdad, sources confirmed to Al Jazeera.
In a separate incident in the Iraqi capital, four mortars landed in the fortified Green Zone, which houses the country's parliament, several ministries and foreign embassies, an interior ministry official said.
A ban on car traffic, initially put in place on Friday for three days in central Baghdad, was lifted less than four hours into the election, a Baghdad security spokesman said.
Two mortar attacks took place in Salahuddin province and in Ramadi in Anbar province, officials said. There were no reports of damage.
At almost exactly the same time, five blasts struck near voting stations in Baquba in the northern Diyala province, officials said. There were no reports of injuries there.
Elsewhere, Al Jazeera's Zeina Khodr, reporting from Sulaymaniyah, in Kurdistan region, said a member of the provincial council of Mosul, Qusay Abbas, was shot dead in the disputed area of Shabak.
"Mosul is a tense city and there is still no real political reconciliation between Arabs and Kurds," she said.
"Today we are seeing a lot of Arabs turning up at the polling stations who want to be part of the political process, from which they have been away for many years, which has weakened them and given Kurds more clout in the Iraqi parliament."
The election is being supervised by as many as 120 international monitors, with a number of foreign embassies providing staff to act as observers.
Al Jazeera's Omar Chatriwala, who accompanied a team of UN monitors on a tour of several cities, saw about 200 people in a polling station on the outskirts of Ramadi at around 9:30am.
"The voting co-ordinator said there had been no problems," he said. "Another co-ordinator, who was in charge of six polling stations, said 3,000 people had turned out to vote in the first couple of hours."
Voters are choosing between a broad range of parties and coalitions and no bloc is expected to win a majority.
After the last national election in 2005, it took the various political parties about five months to agree on a prime minister and for a cabinet to be approved.
Mike Hanna, Al Jazeera's correspondent in Baghdad, said: "In the past, people have tended to vote along sectarian lines. But now, no governing coalition can come to power unless it has the widest possible breadth of support.
|Voters queue at the entrance to a polling station in the Iraqi city of Basra [AFP]
"So political parties and coalitions have been fighting a campaign not on sectarian issues, but on the wider issues of Iraqi nationalism."
Al-Maliki is taking on political opponents tapping into exasperation with years of conflict, poor public services and corruption, and hoping to gain support from a once-dominant Sunni minority.
Iyad Allawi, a former prime minister who heads the cross-sectarian, secularist Iraqiya list, is already complaining about irregularities in early voting, setting the scene for possible challenges to the election's integrity.
Hasan Salman, a representative of the Iraqi National Alliance (INA) - the successor of the United Iraqi Alliance, which has dominated the government since the December 2005 elections - also claimed voting irregularities.
"The government is using its power to steer things to its interest," he told Al Jazeera.
"We are scared the result will be fraudulent. There are 19 million Iraqis qualified to vote, but there are 25 million voting slips, and we still have not received an answer why extra 6 million slips were printed."
The Iraqi electoral commission is to announce preliminary results on March 10-11, based on votes from about 30 per cent of the polling stations.
The supreme court would then certify the poll results, after hearing appeals, within about a month of the election.