The mistake is a setback which will be fixed as the political process is heading in the right direction, Xinhua quoted Maliki as saying in a televised speech.
Maliki said the Deputy Speaker Abadi's nomination was "a dangerous violation to the country's constitution".
Maliki confirmed that his bloc has filed a lawsuit with all the required evidences to prove that the State of the Law coalition is the largest bloc in the first session of the parliament.
"The external collaboration was disclosed when we rejected the constitutional violation, the American administration stood at the side of those who violated the constitution," Maliki said, accusing his political rivals of collaborating with the US to confiscate the elections results.
Maliki's remarks came after the US Vice President Joe Biden called up Haidar al-Abadi and conveyed Obama administration's greetings to Iraq's new leadership.
"Haidar al-Abadi is only representing himself and does not represent the State of the Law Coalition," Khalaf Abdul Samad, a member of Maliki's Dawa Party, said.
Earlier in the day, Iraqi President Fuad Masoum asked Deputy Speaker Haidar al-Abadi to form the next government, but the politicians allied to incumbent Prime Minister Nuri al-Maliki rejected the premier-designate, raising concerns about a political struggle in the country facing insurgency from Sunni jihadists.
The state-run Iraqiya channel showed Masoum signing a letter granting power to form the next government to Abadi, the Shia coalition's nominee for prime minister.