This approach, known in Najaf as the “quietist” tradition, has distinguished Iraq from Iran, and Najaf from Iran’s holy city of Shiite scholarship, Qom. It is part of a historical rivalry between the two ancient cities of Shiite scholarship, one that an official in Najaf described as being “like Oxford and Harvard.”

But amid the current crisis gripping Iraq, from the war with the Islamic State to government corruption and the threat Iranian-backed militias and their political leaders pose to Mr. Abadi and the Iraqi state, Ayatollah Sistani has made a new calculation.

“In recent months he felt a great danger on the political and security scene,” said Ali Alaq, a Shiite lawmaker in Baghdad. “He felt a patriotic duty to act,” he continued, and using an honorific for the ayatollah added, “Sayyid Sistani represents the conscience of the Iraqi people.”

So far, though, Ayatollah Sistani’s push for reforms, while embraced by Mr. Abadi, has borne little fruit, underscoring the opposition among the prime minister’s rivals and the depths of corruption and dysfunction. Mr. Abadi has reduced the salaries of lawmakers and the number of their bodyguards, and has eliminated several high-level positions, including deputy prime minister and vice president, but there has been no serious effort yet on corruption or reforming the judiciary.

Last year, Ayatollah Sistani issued a widely heeded call for young men to take up arms against the Islamic State. But that fatwa resulted in a constellation of new militias, and the growth of existing ones that are controlled by Iran rather than the Iraqi state. The influence of Iran and its militias in Iraq has grown as they have become essential to the fight against the Islamic State, also known as ISIS or ISIL.

Ayatollah Sistani has become increasingly concerned that those militias are a threat to the unity of Iraq, experts say, in part because many of the militia leaders and their affiliated politicians have challenged efforts by the government to reconcile with Iraq’s minority Sunnis, a priority for the clerical leader.