Prime Minister Haider al-Abadi on Sunday announced a reform programme in response to weeks of protests and a call from Sistani, and parliament approved the plan along with additional measures two days later.
"We appreciate that, and hope that these decisions are implemented in the near future," Sistani said in remarks delivered by his representative Abdul Mahdi al-Karbalai.
"We would like to point out that one of the most important requirements of the reform process... Is reforming the judiciary, as it is an important pillar in completing the package of reforms, and there cannot be true reform without it," he said.
Both were billed as initial reform packages, implying that more are to follow.
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Amid a major heatwave that has seen temperatures top 50 degrees Celsius (120 degrees Fahrenheit), protesters have railed against the poor quality of services, especially power outages that leave just a few hours of government-supplied electricity per day.
Thousands of people have turned out in Baghdad and cities in the Shiite south to vent their anger and pressure the authorities to make changes.
Their demands were given a boost last week when Sistani, who is revered by millions, called for Abadi to take "drastic measures" against corruption, saying the "minor steps" he had announced were not enough.
Even with popular support for change, the entrenched nature of corruption and the fact that parties across the political spectrum benefit from it will make any efforts extremely difficult.
Abadi warned on Wednesday that the reform process "will not be easy; it will be painful," and that corrupt individuals would seek to impede change.