His replacement, Haider al-Abadi, has already been asked by Iraq’s president to form a new government.
Nouri al-Maliki was under intense pressure to make way for Haider al-Abadi, a deputy speaker of parliament.
An offensive led by Islamic State (IS) rebels in the north has triggered a security and humanitarian crisis.
Nouri al-Maliki’s spokesman, Ali Mussawi, told AFP news agency that the outgoing Shia Muslim prime minister would drop his bid to remain in his post.
“Maliki will withdraw the complaint against the president and will back the prime minister designate,” he said.
The move, also confirmed by Shia Muslim members of parliament to AP news agency, was announced by state TV.
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