BAGHDAD — Facing widespread protests against government corruption and poor services, as well as a crucial call for change from the country’s top Shiite cleric, Prime Minister Haider al-Abadi proposed on Sunday to radically reshape the dysfunctional political system of Iraq that has been entrenched since the American-led invasion in 2003.

The proposals, which came as the war against Islamic State militants has stalled in western Anbar Province, are wide-ranging and include a new corruption inquiry and the elimination of what has been a hallmark of the American-imposed system: sectarian and party quotas in the appointment of top officials. Dramatically, Mr. Abadi also vowed to eliminate the three vice presidency positions, largely ceremonial jobs that come with expensive perks.

Those jobs are currently held by three figures who have dominated Iraqi politics since the United States toppled Saddam Hussein’s regime: the former prime minister Nuri Kamal al-Maliki, a Shiite; Ayad Allawi, a Shiite whose Sunni-dominated bloc won the most seats in national elections in 2010; and Osama al-Nujaifi, a prominent Sunni Arab leader.

“We are witnessing the end of the post-2003 Iraq,” said Maria Fantappie, the Iraq analyst for the International Crisis Group.