Al-Jaafari's stunning reversal appeared to mark a breakthrough in the months-long struggle to form a national unity government to try to curb the country's slide toward anarchy and enable Washington to begin bringing its 133,000 troops home.
"The one thing I cannot compromise is my dedication to this heroic people," al-Jaafari told the nation in a televised address. "I cannot allow myself to be an obstacle, or appear to be an obstacle to that. I want to be assured of the path of the alliance, which represents the will of the people."
Al-Jaafari said he agreed to a new vote so that his fellow Shiite lawmakers "can think with complete freedom and see what they wish to do."
The Shiite alliance, the largest bloc in the 275-member parliament, must now choose a replacement from a field that lacks stature and power, raising questions whether the new prime minister will be any more successful than al-Jaafari in confronting sectarian violence and the brutal insurgency.
Alliance leaders were to meet Friday to decide how to choose a nominee. If representatives of the seven alliance parties cannot reach a consensus on a single nominee, they will put several choices to a vote before the bloc's 130 parliament members Saturday, officials said.
It was unclear whether al-Jaafari's supporters would insist on him being among any candidates put to a vote, since he did not explicitly say he was out of the running.
The final choice would be presented to parliament later Saturday.
In other recent developments:
Because of the parliament session, Talabani asked Jordan's King Abdullah to put off a reconciliation conference between Iraqi Sunni, Shiite and Kurdish religious leaders, set for Saturday in Amman.
It was unclear why al-Jaafari decided to relinquish the nomination that he won by a single vote during a ballot among Shiite lawmakers two months ago with backing from radical anti-American cleric Muqtada al-Sadr. Al-Jaafari had insisted Wednesday that stepping aside was "out of the question."
In a statement, al-Jaafari said he was ready "to sacrifice myself in any position of responsibility in the service of our people" and would abide by the alliance's decision for the sake of Shiite unity.