Salih made his remarks during a televised speech amid a new wave of protests calling for better basic services and denouncing corruption, Efe news reported.
"Abdulmahdi said he accepted to submit his resignation and called on the political blocs to agree on an acceptable replacement," Salih said.
"We started working on a new electoral law that convinces the Iraqis, fixes the previous law's issues and allows more fair elections that better present the people's interest, including the young people right to run for the elections," he added.
"The current situation cannot continue, we need serious reforms and major changes that must be undertaken," he added.
A new electoral commission will replace the existing one.
"I want to confirm that I as President of the Republic will accept to (hold) early elections by approving the new electoral law and the new electoral commission," he added.
The president showed support for the demands of the protesters, adding that "repression is rejected; employing force and violence is rejected."
He called for those who used "excessive force" during the most recent rallies to be held to account and for legal proceedings to take place.
At least 100 people were killed while over 5,000 were injured when the second wave of protests broke out on 25 October, according to the Iraqi High Commission for Human Rights.
Last Friday marked the return of mass demonstrations that rocked Iraq at the start of the month amid anger over unreliable electric and water services, lack of economic opportunities and pervasive corruption.
The Higher Ministerial Committee formed to investigate civilian deaths during the initial protests revealed in its final report that 157 people died, including eight members of the security forces.
( With inputs from IANS )