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Appearing on state television flanked by Abadi and other Shi'ite politicians, Maliki spoke of the grave "terrorist" threat from Islamic State Sunni militants before giving up on his fight to stay on.
"I announce before you today, to ease the movement of the political process and the formation of the new government, the withdrawal of my candidacy in favour of brother Dr. Haider al-Abadi," said Maliki.
Abadi is seen as a far less polarising figure who has a chance of uniting Iraqis against Sunni insurgents who have captured large parts of the country in the north and west - including Iraq's largest dam and five oil fields.
The announcement is likely to please the Sunni minority which dominated Iraq under Saddam Hussein's iron-fisted rule but was then sidelined by Maliki, a relative unknown when he came to power in 2006 with strong U.S. backing.
The man who plotted against Saddam for years from exile drew comparisons with his former enemy, who had launched brutal crackdowns on Shi'ites and Kurds.
Critics accused Maliki of being an authoritarian leader with a sectarian agenda that drove Sunnis, including heavily-armed tribes, into the Islamic State camp and revived a sectarian civil war.