Maliki spoke for about 25 minutes at a ceremony held in a sports arena, The Washington Post reported.
"I'm telling you, Iraq is for all those who believe in the democracy," he said.
The prime minister also sent a text message to Iraqis.
"All of us are for Iraq glory and pride in the nation. I congratulate you and our Iraqi people on this historic day. With love, and with my respect to you and your honorable family, your brother, Nouri al-Maliki," he wrote.
U.S. troops pulled out two weeks ago. Since then, the country has shown some signs of fraying along sectarian lines.
Two provincial Shiite leaders announced Saturday they are withdrawing from the opposition al-Iraqiya bloc, which has the support of many Sunni Muslims. Both said they are considering joining Maliki's coalition, the State of Law bloc.
Notable deaths of 2014 [PHOTOS]