Abadi called on "the judicial authority to undertake a series of drastic measures to guarantee judicial prestige and independence and allow it to fight corruption," his office said in a statement.
He said such measures are necessary for his proposed reforms, which are aimed at curbing corruption, streamlining the government and improving services, to be carried out.
"The wide reforms I called for require a just and impartial and firm judiciary to support these reforms," Abadi said.
"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.
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"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.
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.
Their demands were given a boost last week when Sistani called for Abadi to take "drastic measures" against corruption, saying the "minor steps" he had announced were not enough.
Various parties and politicians have sought to align themselves with the protesters in order to benefit from the movement and mitigate the risk to themselves.
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.