The constitution will now be approved if a simple majority of all those who turn out to vote say yes and if two-thirds of voters in at least three provinces do not vote no.
The move was approved by 119 of the 147 MPs present.
The change had said two thirds of “registered voters” would be required in three provinces to block the charter, but the new decision has changed this back to read just “voters”.
This was seen as lessening the chances for the increasingly alienated Sunni Arab minority to vote down the charter.
Many Sunnis object to it on the grounds that its federalist principles will pave the way for the break-up of the country, handing over oil-rich provinces to Kurds and Shiites.
Sunnis welcome decision
The charter has caused deep divisions between the Sunnis and the rival majority Shiites and their Kurdish allies who now dominate parliament.
The parliamentary U-turn “is a good decision because the changes were not correct. Unfortunately the deputies sent the wrong message to the electorate by trying to cheat on the text,” said Salah Motlak of the National Dialogue Party, a Sunni group.
The once all-powerful Sunnis, who are believed to form the backbone of the ongoing insurgency, might have enough registered voters in three provinces to torpedo the constitution, though many have called for a boycott of the vote.
Al-Qaeda’s Iraq branch, headed by Iraq’s most wanted man Abu Musab al-Zarqawi, has also urged Sunnis to boycott the referendum.
Hilla blast kills 25
Meanwhile at least 25 people were killed and 87 wounded when a car bomb exploded late Wednesday near a mosque as Shiites gathered for prayers in Hilla, a town south of the Iraqi capital.
“Many dead and wounded have been pulled out of the rubble and there are 25 dead and 87 wounded. The search is continuing,” said an official of the rescue services for Babil province.
Half of the roof of the historic building, which was restored three years ago, collapsed due to the force of the blast, while several nearby shopfronts were damaged.
The attack came as men, observing the first day of the holy month of Ramadan, were gathering for prayers at the end of a day of fasting.
The new strike comes after at least 10 people were killed by car bomb explosion on Friday in a vegetable market in Hilla, 100 kilometres from Baghad.