"The committee discussed all the documents and evidence that prove that there was some manipulation in voting stations," Hassen al-Senaed, a parliamentarian in Maliki's bloc, said.
"We expect an increase in our number of seats in Baghdad. The manipulation included the changing of signatures and the removal of names and numbers and changing of ballots."
It has been more than a month since Allawi's secularist coalition won 91 seats, edging out the State of Law coalition of al-Maliki, by just two seats.
However, no party has gained enough seats to rule over the country on its own and the blocs have been involved in negotiations in an attempt to form coalitions able to create a working majority in parliament.
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"Al-Maliki's bloc wanted a manual recount in five provinces," Zeina Khodr, Al Jazeera's correspondent in Baghdad, said.
"They said they discovered irregularities [in the voting] and that 750,000 votes were manipulated.
"According to them it could change the outcome of the election, as it was such a close race," she said.
Before the recount, State of Law won 26 seats to 24 for Allawi's Iraqiya in Baghdad.
Ad Melkert, the UN special representative to Iraq, last month described the polls as "credible" after the electoral commission said there was no evidence of systematic or widespread fraud in the counting of ballots.
The judicial panel that ordered the Baghdad recount was established by the electoral commission to handle complaints from aggrieved parties about the conduct of the election.
Maliki's State of Law and the Iraqi National Alliance (INA), a Shia-led bloc that secured 70 seats in the election, have been seen as inching towards an agreement that could sideline Allawi.
However, Ammar al-Hakim, the leader of the Supreme Islamic Iraqi Council, which is part of the INA, said on Monday that said he did not see either al-Maliki or Allawi as having enough support, inside and outside Iraq, to become the next prime minister.
"We are talking about a person who should be accepted on a national level," he said.
"This is the most important point because the prime minister is not going to be a prime minister of his own party or his political movement, but for all of Iraq.
"On such a basis, we find it's difficult for Mr Maliki or even Mr Iyad Allawi to gain the needed acceptance."
Maysoun Damlouji, Iraqiya's spokeswoman, dismissed al-Hakim's claims that Allawi did not have widespread support.
"We got a huge number of votes, which means he is accepted," she said.
"We are the only bloc that has the diversity; we have Arabs, Kurds, Turkomen, we have them all, so if there is one who is widely accepted it is Mr Allawi."