The bill, the Jaafari Personal Status Law, sets out rules to do with inheritance, marriage and divorce.
Supporters of the draft, named after a Shiite Muslim school of jurisprudence, say it simply regulates practices already existing in day-to-day life.
Opponents say the bill represents a step back for women's rights in Iraq, and worry that it could further fray already fragile sectarian ties between the country's various communities amid heightened violence ahead of April parliamentary polls.
Critics point in particular to a clause of Article 147 in the bill which allows for girls to divorce at the age of nine, meaning they could conceivably marry even earlier, and another article which would require a wife to have sex with her husband whenever he demands.
An Iraqi man walks past a banner reading in Arabic, "the Jaafari law (Jaafari Personal Status Law) we will not abandon it because it is our identity", in Baghdad. (AFP Photo)
Other clauses have been ridiculed for their specificity, from the conditions under which mothers must breastfeed their children to how many nights a polygamous man must spend with each wife and how he may use additional nights.
But the part of the bill that has provoked by far the most anger has been the one regarding the marriage and divorce of young girls in Iraq, where a quarter of women are married before the age of 18, according to a 2013 study by the Washington-based Population Reference Bureau.
Analysts have, however, dismissed the bill as politicking, and say it is highly unlikely to make it through Iraq's Council of Representatives.
'Violation of children's rights'
"The draft law is a humanitarian crime and a violation of children's rights," said Hanaa Edwar, a well-known activist and head of the charity Al-Amal ('Hope' in Arabic).
"It turns women into tools for sexual enjoyment. ... It deletes all their rights."
Edwar's criticism has been echoed by a wide variety of opponents, ranging from domestic foes to New York-based Human Rights Watch (HRW) and even the UN envoy to Iraq who said the bill "can contribute to the fragmentation of the national identity."
An Iraqi woman walks with her daughter in Baghdad. (AFP Photo)
"The bill will reverse the gains made to protect and advance women and girls' rights that are protected by the constitution," Nickolay Mladenov said in a statement this month.
It has also faced opposition from religious leaders, with Bashir Najafi, one of Shiite Islam's most senior clerics, issuing a fatwa this month saying the bill has several "legal and doctrinal" problems which "no scholar can agree with".
The bill's defenders, however, say the new law would not strike down Iraq's current Personal Status Law, lauded as one of the most progressive in the region.
They also point to the country's constitution as giving them the freedom to legally regulate personal status within the Shiite Muslim community.
"The idea of the law is that each religion regulates and organises its personal status depending on what it believes," said Ammar Toma, a Shiite MP from the Fadhila party which is the bill's principal backer.
Toma said the law would modernise age-old practices of looking to local leaders for rulings on marital disputes, arguing that "instead of keeping the matters of marriage in that old style, the law moves the issues to state institutions and brings a system of modernity."
'Maintains women's dignity, rights'
Justice Minister Hassan al-Shammari, also a member of Fadhila, has meanwhile argued that the law contains other articles which provide "basic guarantees for maintaining women's dignity and rights".
A banner reading in Arabic "the Jaafari law (Jaafari Personal Status Law) is my glory and my pride" in Baghdad. (AFP Photo)
The fierce debate may, however, turn out to be moot, with analysts predicting that the bill is unlikely to be passed before legislative elections next month, if at all.
Indeed, according to a senior government official who declined to be named, one of the main reasons it was endorsed by cabinet was because Prime Minister Nuri al-Maliki, a Shiite, did not want to be criticised for failing to back a demand from within the majority community ahead of the polls.
Maliki could also be looking to leave open the possibility of a post-election alliance between his State of Law coalition and Fadhila, as no single party is expected to win a majority in parliament on its own.
"There is a political dimension to this draft," said Ihsan al-Shammari, a professor of politics at Baghdad University.
"Everyone is looking to win votes and wants to appeal to their base," he said.
"Submitting this bill -- at this moment -- is for political and electoral reasons."