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He said his decision was aimed at preserving the country's "unity".
"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," Maliki said in his Thursday address, Aljazeera reports.
Maliki's announcement came days after he refused to stand down and threatened to challenge the Iraq president's decision to appoint Abadi as his successor.
"Maliki will withdraw the complaint against the president and will back the prime minister designate," Ali Mussawi, Maliki's spokesman, told the AFP news agency, referring to a lawsuit the outgoing premier had vowed to file.
Al Jazeera's Jane Arraf, reporting from Erbil, said Maliki's move was influenced by the statement of Ira's most senior Shia religious leader, Ayatollah Ali al-Sistani.
"When all the odds were stacked against him, when the US and Iran as well as European countries and almost every political faction in Iraq was telling him that he had to go, he still persisted on hanging on," Arraf said.
"The thing that really clinched it though was that the statements by Iraq's top Shia religious authority, the Marjaya, specifically the Ayatola Ali al-Sistani - absolutely revered by Iraqi Shias - who indicated in a very rare statement that he thought it would be better for the country if Maliki did indeed step aside."