But only 202 members of parliament out of 329 were present, which is less than the necessary two-thirds quorum needed to choose a new president for the mostly ceremonial post, while 126 lawmakers boycotted the session.
Twenty-five candidates, who have been approved by the Iraqi Parliament, are running for the role, including Mr Salih.
Insurgents killed hundreds of Shias to undermine the government and trigger a wider sectarian conflict.
His exemplary personal history, foreign affairs experience, and regional political experience played a huge role in helping him secure the votes to become president of Iraq.
As in the previous two aborted votes, last Saturday and Feb.
As president, Salih faces one conflict after another for pushing for the reconstruction of the country.