"Since my position about this current candidacy is considered unconstitutional, I place my readiness to resign from the presidency in front of the members of parliament so they can decide based on their responsibilities as representatives of the people," Salih said in a letter to the MPs on Thursday.
He said he would rather step down than pick a Prime Minister that protesters reject, so Parliament will now have to vote on the matter, reports Efe news.
Salih's decision came as hundreds of demonstrators have taken to the streets in Baghdad and other southern cities to demand the next Prime Minister be independent.
The Al-Binaa coalition, headed by Hadi al-Amiri, put forward Asaad al-Eidani, current Governor of Basra, as its chosen candidate to form a government.
"Out of my keenness to stop blood and maintain civil peace, and with all due respect to Asaad al-Eidani, I refuse to nominate him," Salih added.
Salih, a Kurdish politician who assumed office over a year ago, said he had taken the decision to ensure the stability of Iraq which has been the scene of anti-government rallies since October 1.
More than 500 people have been killed in the demonstrations.
The designation of a candidate without making sure which bloc has the biggest number of seats in parliament "may be viewed as a violation of the Constitution", according to Salih.
"The presidency has received several contradictory letters on the majority bloc in Parliament," he continued.
Another parliamentary bloc, al-Fath, last week nominated outgoing Minister of Higher Education Qusay al-Suhail to be the premier, a proposal that angered protesters.
Abel Abdel Mahdi resigned last month as Prime Minister after pressure from protests.
On December 23, a constitutional deadline to pick a premier-designate expired amid disputes among rival parliamentary blocs.
( With inputs from IANS )