Maliki has come under fire recently for enacting measures that some lawmakers and political opponents see as an attempt to monopolize power going into provincial elections set for April, The New York Times reported.
Two members of Iraqiya, a largely Sunni bloc of lawmakers, called for Maliki, a Shiite, to step down.
"The option of early elections will avoid many problems," Saleh al-Mutlaq, a deputy prime minister who is a Sunni, said in a statement on Friday. "The current government must hand in its resignation."
Ayad Allawi, the leader of Iraqiya but a secular Shiite, said the current government was incapable of change and "must submit its resignation so the Iraqi political powers can find solutions for the problems."
Maliki's media adviser Ali al-Musawi said the government supports early elections.
"In a normal state, the opposition will be the ones that call for early elections or dissolving" the government, Musawi said. "Now we are calling for dissolving them."
Dawa, the ruling party, has not yet commented on the situation.