In the crucial province-by-province tally, al-Maliki has been ahead throughout the race, winning in seven out of Iraq's 18 provinces to Allawi's lead in five.
The parliamentary elections, Iraq's second only for a full-term parliament since the 2003 US-led invasion, will determine who gets to form the next government that will rule as American soldiers leave.
Allawi's Sunni support is likely due to his non-sectarian stance and repeated condemnations of the influence of Iraq's powerful Shia neighbour, Iran.
In an interview with Reuters news agency on Friday, Allawi said he would not accept a return to al-Maliki's "one-man rule", indicating a long struggle in the shaping of a new government.
"Our concern really is the welfare and well-being of the people, regardless of what kind of shape the government will take or how long it's going to take," Allawi said.
"Because we are not going to accept forming a very quick government ... that would bring the same disasters of the last four years again to Iraq. The rule of one party, one-man rule, we don't accept this."
However, Allawi did not rule out sharing power with al-Maliki conditionally. "If he changes his attitude not by words but by deeds ... then of course we'll be very willing to co-operate with him," he said.
"The dynamics have changed, maybe this will alert him that he will have no future if he persists in whatever he has done."
The vote counting has been a long process, with results being portioned out piecemeal by election officials and almost immediately subject to fraud accusations.
Parliament seats are apportioned mainly by how well coalitions do in the provinces, not according to overall vote.
With so much at stake, several leading candidates have raised accusations of fraud. Al-Maliki's bloc accused election officials of doctoring the vote counts and called for a recount on Tuesday.
Qassim al-Aboudi of Iraq's electoral commission sought to assure all candidates of the fairness of the election process the following day.
"We reassure all the political entities that the electronic counting centre is rechecking all the results counts from all the provinces," he said.