Early Iraq poll results suggest close contest
Mr Maliki leads in two Shia provinces south of Baghdad while Mr Allawi is in the lead in two provinces to the north.
A BBC correspondent in the Iraqi capital says both men were expected to do well in those places and many votes are still to be counted.
But there have been complaints about the count and some claims of fraud.
The partial results come four days after balloting.
Final results for all 18 provinces are not expected for a fortnight.
The Independent High Electoral Commission’s results showed Mr Maliki’s State of Law coalition leading in Najaf and Babil and Mr Allawi’s secular Iraqiya alliance ahead in Diyala and Salahuddin.
There were expectations that more results would have been announced by now, and that has led to growing questions over the process, our correspondent says.
Officials ’overwhelmed’
Iraqiya has listed a series of alleged violations, saying some of its votes had been removed from boxes and replaced by other ballots.
"Insistence in manipulating these elections forces us to question whether the possibility of fraudulent results would make the final results worthless. We will not stand by with our arms crossed," a statement from the alliance said.
The election commission says it will look into complaints of fraud, but officials say they are overwhelmed by the task of counting votes.
About 6,200 candidates from 86 factions campaigned for seats in the 325-member parliament.
Analysts say it is unlikely one party will form a government alone and there may be months of negotiations on a coalition.
Voter turnout was 62%, officials said, despite attacks that killed 38 people on Sunday.
It was down on the 75% turnout figure for the 2005 general election.
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