BAGHDAD—In a few hours last month, Iraqi Prime Minister Haider al-Abadi reversed a year of mounting criticism and became the resolute leader many Iraqis and his Western allies were demanding.

Yet after stunning Iraqis by announcing a plan to tackle corruption and streamline government, he has backtracked on his most ambitious reform pledges under pressure from Shiite Muslim hard-liners backed by Iran, Western and Iraqi officials said.

Little...