"If article 61 of the interim constitution is not changed, Imam (Ayat Allah Ali) Sistani may issue a fatwa declaring illegitimate all those (Iraqis) to whom power is transferred in June," said Ayat Allah Muhammad Baqir al-Mohri in comments published on Saturday.
Sistani "may also order the Iraqi people to protest or carry out major popular demonstrations and sit-ins in all Iraqi cities," added Mohri.
The Kuwait-based aide to Sistani did not elaborate on the changes to article 61 wanted by Sistani.
Sistani had complained that veto guarantees enshrined in the constitution could constrain the power of the Shia. He also says a proposed three-person presidential council, comprised of a Shia, a Sunni and a Kurd, is a recipe for religious and ethnic squabbling.
Mohri's comments, made at Friday prayers in Kuwait, were carried by Kuwait newspapers on Saturday.
"If article 61 of the interim constitution is not changed, Imam (Ayat Allah Ali) Sistani may issue a fatwa declaring illegitimate all those (Iraqis) to whom power is transferred in June"
Ayat Allah Muhammad Baqir al-Mohri
The interim constitution and how to transfer power from US occupation forces to a sovereign Iraqi government has been a subject of intense debate among Shia, who were oppressed for decades by ousted President Saddam Hussein's government.
The US-appointed Governing Council signed the interim constitution at the start of March despite several delays and over the objections of Sistani.
Washington has been pushing for progress on the constitution and the make-up of a new government in order to meet a 30 June deadline to hand over sovereignty.
Mohri also urged the United Nations and the US occupying authorities running Iraq not to disagree with Sistani, "or else there will be pandemonium in Iraq, and protests and chaos will be widespread".
Earlier this month, Sistani in a letter urged the UN not to endorse the interim constitution, raising a potentially grave obstacle to US plans to hand power to Iraqis.
"Imam Sistani has decided not to meet with United Nations envoy Lakhdar Brahimi until after declaring illegitimate the interim Iraqi constitution which divides Iraq," Mohri said.