State of Law appeared to have won in all nine southern Shia provinces, as well as Shia east Baghdad, and was "competing for second or third" place in other provinces, a government official close to the prime minister said.
If confirmed, the results in the second major election since the 2003 fall of Saddam Hussein would overturn six years of provincial rule by mostly religious parties and give al-Maliki strong momentum in his bid to hold on to power in a general election due this year.
Iraqi and US officials have hailed the elections as a success, with Barack Obama, the US president, praising the polls and al-Maliki calling them "a victory for all the Iraqis".
Almost 300,000 local and international observers monitored the elections and the independent electoral commission said it had received very few complaints about attempts of vote-buying.
But only about half of eligible voters cast ballots in the polls and there have been allegations of irregularities.
Voter turnout was 51 per cent - lower than the 55.7% who voted four years ago amid sectarian violence that targeted polling stations, according to the electoral commission.
Hundreds of thousands of eligible voters out of 15 million eligible to vote in 14 of the country's 18 provinces were reported to have been left off ballot lists. Election officials have said they will investigate.
Mithal al-Alusi, a Sunni legislator, said there were "many mistakes in this election committee".
|Obama said a 'substantial' part of the 140,000 US troops would be home in a year [AFP]
"We are very worried about a few hundred thousand voters [who] didn't become approved to vote or [get] the chance to vote."
He also accused Iranian diplomats in Iraq of interfering in the polls, saying Iranian diplomats moved freely among polling stations during the voting and "we know they gave advice".
Ahmed Chalabi, head of the Iraqi National Congress, agreed that "several hundred thousand people were denied the vote, but I believe it was not intentional".
He said "a shortcoming in the electoral commission's preparations" was to blame.
"Iraq is free now, the American occupation is ended, President Obama is pulling out the troops faster than was agreed," Chalabi told Al Jazeera.
Obama said on Sunday that a substantial number of the 140,000 US troops in Iraq would be home within a year.
The US signed a status of forces agreement with Iraq last year that set a 2011 deadline for US forces to leave the country.
But the new US president, who held talks with the Joint Chiefs of Staff at the Pentagon last week, told US network NBC television that Iraqis were now ready to take more responsibility for their own security.
"I think we have a sense, now that the Iraqis just had a very significant election with no significant violence, we are in a position to put more responsibility on the Iraqis," he said.