The results announced by Iraq's electoral commission showed that Allawi had a narrow lead of about 9,000 votes over al-Maliki's bloc.
The country's proportional representation system makes it unlikely that any single group will clinch the 163 seats needed to form a government on its own, and protracted coalition building is likely.
Once the electoral commission announces the final poll results, the country's supreme court will have to certify them - after hearing appeals - within about a month of the election.
'Neck and neck'
Anita McNaught, Al Jazeera's correspondent in Baghdad, said that now that 80 per cent of the vote had been counted it was possible to see a pattern emerging, and showed the race would be "neck and neck".
"It would be a safe assumption to make that many Shias are voting for a party that includes Sunni on the ticket," she said.
"Perhaps we are seeing the beginnings of a unifying trans-sectarian voting pattern in Iraq. Perhaps we are seeing the public reach across the sectarian divide.
"There are still the overseas votes to come in that are thought to be in favour of Allawi. If they are neck and neck right up to the 100 per cent domestic vote, that could tip things in favour of Allawi."
Our correspondent said another dimension to the election, and something that "might have the Kurds rather worried", is that one of the five provinces in which Allawi is scoring ahead is Kirkuk.
"The constituency that backs Allawi is absolutely vehemently opposed to anything other than Kirkuk remaining a part of Iraq," she said.
Al-Maliki's coalition is ahead in oil-rich Basra and Karbala, two of Iraq's three biggest provinces, which have Shia Muslim majorities.
His State of Law is also holding on to leads in Baghdad, whose 70 seats account for more than a fifth of Iraq's 325-member Council of Representatives, as well as Babil, Najaf, Wasit and Muthanna.
Claims of fraud
Since the March 7 election, the counting process has been fraught with claims of fraud, mostly from the opposition.
The IHEC has also been criticised for being chaotic and slow in releasing the results.
Meanwhile, violence continues to claim lives around the country.
Eight Iraqis were killed and 11 others wounded when two bombs exploded in separate attacks five minutes apart in the town of Mussayab on Tuesday, police said.
The bombs were attached to two cars carrying passengers on the main street of Muassayab, which is about 60km south of Baghdad.