Reporting from Damascus, the BBC's Natalia Antelava says some Iraqis living in Syria criticise Mr Maliki for ignoring their problems, for failing to secure their return and for deepening Iraq's sectarian divisions.
Among Iraqi expatriates in Syria there are many Sunnis Arabs and many former members of Saddam Hussein's Baath party.
Many say that it is too dangerous for them to return to Iraq while it is ruled by a Shia prime minister, our correspondent says.
She says that for his part Mr Maliki believes former Baathists are trying to undermine security gains made by his government by staging attacks back in Iraq.
The elections are seen as a crucial test for Iraq's national reconciliation process ahead of a planned US military withdrawal in stages.
There has been pre-election violence and insurgents have vowed to disrupt the poll. On polling day itself, more than 200,000 security personnel will be on duty in Baghdad.
The BBC's John Simpson visits a market in Baghdad's Doura district
Travel around the country has been restricted and the authorities have cancelled all leave for security services.
On Thursday at least 14 people were killed in Baghdad as suicide bombers attacked two polling stations in different parts of the capital. Earlier in the day, a mortar attack on a crowded market killed seven.
Security forces, detainees and hospital patients were able to vote on Thursday. There was a reportedly high turnout, with estimates suggesting 800,000 people cast ballots.
On Wednesday, three suicide bombers attacked police and a hospital in Baquba, a city north of Baghdad, killing at least 30 people.
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