But in his first policy speech, Maliki called for Iraq's powerful militias to be merged with US-trained security forces - an explosive issue in the country because militias are tied to political parties and operate along religious lines.
"Arms should be in the hands of the government. There is a law that calls for the merging of militias with the armed forces," said Maliki, nominated by the ruling Shia Alliance.
The United States hopes a national unity government will foster stability in Iraq and enable it to start bringing home its more than 130,000 troops.
"This is a good day for Iraq. It is an important day for Iraq," US secretary of state Condoleezza Rice said in a conference call with reporters in Washington. "This is someone with whom we can work."
Five US soldiers were killed by a roadside bomb south of Baghdad on Saturday, the US military said in a statement. A total of 2,385 US soldiers have been killed in Iraq since the March 2003 US-led invasion to topple Saddam Hussein.
The Shia Alliance chose Maliki after its original candidate, interim Prime Minister Ibrahim al-Jaafari, bowed out. Other parties opposed Jaafari on grounds he was too weak. Iraqi President Jalal Talabani formally designated Maliki as prime minister after a breakthrough in negotiations on Friday and asked him to form Iraq's first full-term government since Saddam was ousted in 2003.
Earlier, parliament re-elected Talabani as president.
Mahmoud al-Mashhadani was elected as parliamentary speaker.