Feb 19 (Reuters) - Iraq's outgoing prime minister urged political leaders on Wednesday to quickly approve his designated successor's cabinet and warned he would walk away from his caretaker post if they do not do so by March 2.

Facing a wave of protests and civil unrest that has claimed the life of almost 500 people since Oct. 1, Prime Minister Adel Abdul Mahdi quit in November. He has stayed on as a caretaker, but says now he's ready to leave, which would create an unprecedented political vacuum at the top of the government.

"It would not be correct or appropriate for me to remain in power after March 2, and I will have no recourse but to implement the text of the constitution and the cabinet's internal bylaws," said Abdul Mahdi, who has already stopped chairing weekly cabinet meetings.

It took Iraq's political leadership until Feb. 1 to agree on Mohammed Tawfiq Allawi to replace Abdul Mahdi, missing a constitutional deadline to appoint one within 15 days of his resignation.

Allawi now takes over a government tasked with organising early elections. The constitution gives him 30 days -- until March 2 -- to present a cabinet to parliament for approval.

He has made little progress as rival political factions squabble over ministerial portfolios. But on Saturday he said he would form a government within the coming week.