A statement from al-Maliki's office earlier on Sunday called for the recount to "preserve political stability and to avoid a deterioration of security and a return of violence which was quelled after much effort and loss of blood".
"March 7 was a big step for democracy in Iraq," the statement said.
"But many political entities are now demanding a recount by hand. This is to protect democracy and to preserve the legitimacy of the electoral process."
In a statement on his website, Jalal Talabani, Iraq's president, endorsed al-Maliki's call to "preclude any doubt and misunderstanding" in the results.
"As the president of the state, authorised to preserve the constitution and to ensure justice and absolute transparency, I demand the Independent High Electoral Commission recount the ballots manually starting from Sunday, March 21," Talabani said.
Saad al-Muttalibi, a candidate from al-Maliki's State of Law coalition, told Al Jazeera that if the results were not checked by hand, it could escalate violence in the country.
"If these people do not understand politics, they should go home, they are creating havoc in the country," he said.
"There is a danger of the country being divided, I am afraid then Iraq will go down in a very violent way, in a way that we do not want to see."
State of Law trailed slightly behind the Iraqiya bloc of Iyad Allawi, a former prime minister, with just over 95 per cent of the votes counted on Sunday.
Iraqiya has accused al-Maliki of trying to intimidate the IHEC by demanding the recount.
"This is a clear threat against the commission that aims to put pressure on it, in order to carry out fraud in favour of [al-Maliki's] State of Law Alliance," Intisar Allawi, a senior candidate of Iraqiya, said on Sunday.
He said that al-Maliki's statement was a "contradiction" prompted by the news that Iraqiya had taken the lead in the nationwide vote tally.
"While he says that the election is accurate, fair and transparent, when Iraqiya takes the lead, he accuses the commission," she said.
Intisar noted that a manual recount "would mean a delay of the results for several months. This would lead to a political vacuum that would affect the security situation".
Iraq's proportional representation system makes it unlikely for any single group to clinch the 163 seats required to form a government on its own.
Results from the election, the second since Saddam Hussein was ousted in the US-led invasion of 2003, come less than six months before the US is set to withdraw all of its combat troops from Iraq.