President Jalal Talabani gave the order to Maliki in Baghdad just one day ahead of Talibani's 15-day constitutional deadline after being re-elected, Alsumaria reported.
Maliki has 30 days to form a cabinet from the embattled country's four main political parties divided by ethnic and religious factions, The Washington Post said.
Since the March 7 national elections were so narrowly divisive, government has foundered and accomplished little, the report said.
The prime minister, leader of the State of Law party, must work with the Sunni Muslim Iraqiya bloc, the Shiite Islamic Supreme Council of Iraq and the Kurdish party.
The past eight months have seen shifting of political alliances between the larger and smaller parties and Maliki was among those who embraced former political foes, the Post said.
The report said his tactics have tentatively been supported by both Washington and Iraq's Shiite-dominated neighbor, Iran.