'Symbol of Iraq'
Khalid al-Attiyah, the deputy speaker of parliament, said that al-Hakim's death was a loss for Iraq.
"We offer our condolences to all the Iraqi people for the death of al-Hakim. He is one of the symbols of Iraq ... we hope political leaders will continue his work," he said.
Christopher Hill, the US ambassador to Iraq, and General Ray Odierno, the top US commander in Iraq, said in a joint statement that throughout his life al-Hakim had demonstrated "courage and fortitude, contributing to the building of a new Iraq".
Al-Hakim had largely withdrawn from the public eye since being diagnosed with cancer, but on his few public appearances he had looked increasingly frail.
The ISCI is currently part of Iraq's ruling Shia alliance, which includes the Dawa party of Nouri al-Maliki, the prime minister, but earlier this week announced it was joining a new alliance for elections next January.
The party has several members in senior ministerial posts, and has influence in Iraq's security forces, which include members of its armed affiliate, the Badr Organisation.
Much of the ISCI's support comes from the influence of the al-Hakim name, which is revered among Shia Muslims for its lineage of scholars and sacrifice during the rule of Saddam Hussein, the executed former president.
Fares Braizat, a political analyst at Qatar University, told Al Jazeera al-Hakim had been an influential player in internal Iraqi politics.
"He has passed away when there is a new Iraqi coalition that excludes al-Maliki, [and] in a situation in which there is a political and diplomatic problem between the Iraqi government and the Syrian government after the blast that hit Baghdad a few days ago.
"All this throws into doubt what is the outcome of the coalition, the relationship between that coalition and Mr Maliki, how the Iranian factor is going to play into Iraqi politics."
"The person who is going to succeed al-Hakim will have to be someone who is very close to Iran to keep the current arrangement in place.
"If that doesn't happen then that will cause a problem to the traditional alliance between the Iranians and the [ISCI]."
The ISCI follows the ideology of the Iranian revolution and receives support from Tehran.