The Independent High Electoral Commission (IHEC) announced on Sunday that State of Law was leading in predominantly Shia Muslim Basra, while Iraqiya was dominating in the heavily Sunni Muslim province of Anbar in the west and in Kirkuk in the north.
The biggest surprise of the day was Kirkuk: with 61 per cent of votes counted, Iraqiya was leading by 3,500 votes over Kurdistania, an alliance of the Kurdish autonomous region's two long-dominant parties.
"In Kirkuk, we have seen the secular coalition of Iyad Allawi edge ahead of the Kurdistan alliance," Al Jazeera's Anita McNaught, reporting from Baghdad, said.
"It's an area that the Kurds claim, that they want to see as part of their Kurdish region. It's one that is hugely contentious.
"We expected to see a concerted effort by Kurds to vote as a block to prove their point - that Kirkuk is a Kurdish region and should therefore be part of their area.
"But ... it looks like many people don't believe that Kirkuk should end up in Kurdish control."
In Anbar, the vote count was 58 per cent so far, and Allawi's coalition was ahead by more than 100,000 votes over State of Law.
Iraqiya was also leading in Ninawa, Iraq's second biggest constituency, and the predominantly Sunni Muslim central provinces of Diyala and Salaheddin.
In the southernmost province of Basra, where 63 per cent of the votes had been counted, State of Law was leading with 219,000 votes, 98,000 ahead of its nearest rival.
The results, broadcast on Iraq's al-Sumaria television, suggested that the race would remain close, though al-Maliki's bloc was leading in the crucial region of Baghdad.
Baghdad is by far the biggest electoral prize in the contest, with 68 seats out of 325 in the new parliament.
In addition to Baghdad, al-Maliki's bloc was leading in early returns from most provinces to the south of the Iraqi capital.
|The election panel is under pressure to tally faster the results of last week's polls [EPA]
In the Shia heartland of Karbala, more than half the results had come in and, as expected, State of Law was also well ahead of its rival coalition.
Elsewhere, figures showed Kurdistania was ahead in the battleground province of Sulaimaniyah and the country's northernmost province of Dohuk.
Earlier figures also put Kurdistania ahead in Erbil, seat of the Iraqi Kurdish regional government.
The Iraqi National Alliance (INA), a coalition of mostly Shia Muslim religious parties, including the largest party in the outgoing parliament, the Supreme Islamic Council of Iraq (SICI), was running a close second in Baghdad behind State of Law.
It was also showing a narrow lead in the southern provinces of Maysan, Diwaniya and Dhi Qar.
'Horns of a dilemma'
Whatever the political picture, the Iraqi electoral panel continues to be under tremendous pressure to deliver more results, and faster.
Al Jazeera' McNaught said: "The talk at the IHEC today has been about the frustration the Iraqis feel about the delays in the results emerging - not entirely fair frustrations but it's still something people are quite heated about.
"The IHEC is caught on the horns of a dilemma - work too slowly, and they risk damaging confidence in the system, making Iraqis suspect that something is wrong.
"But work to fast, push the process and make mistakes, and you destroy faith in the entire vote count."