The decision made on Friday amid a crunch meeting of Iraq's US appointed interim Governing Council, which was battling on Saturday to draft a temporary constitution by a midnight deadline, prompted several Islamic councillors to storm out in protest.
The women also want at least a 40% stake in the country's evolving political power, which will be enshrined in the transitional law under discussion, said Jamil al-Jawahiri, a spokesman for Iraqi al-Amal Association, one of the groups leading the campaign for greater women's rights in Iraq.
But several women questioned on the street in Baghdad were sceptical that the political wrangling would have any real impact on their conservative lives.
Successful lobbying by the heads of 17 Iraqi women's groups at a meeting on Thursday prompted 15 council members to repeal a proposal to scrap Iraq's 1959 family affairs code - considered among the most progressive in the Middle East - and place it under Muslim religious jurisdiction, Jawahiri told AFP.
"It is a good day for everyone, not just for women," he said. "Women have shown they can get what they want by being organised and good lobbyers and not through using violence."
"It is a good day for everyone, not just for women. Women have shown they can get what they want by being organised and good lobbyers and not through using violence"
Iraqi al-Amal Association
Jinan al-Ubaidi, in charge of women's affairs for the Supreme Council of the Islamic Revolution in Iraq (SCIRI), Iraq's main political party, in the holy city of Najaf, was not so pleased.
"The repeal is a great loss for the Iraqi society because it gives freedom to all religious communities," she said.
Last December, the US-picked Governing Council voted to ditch the law, which makes polygamy difficult and guarantees women's custody rights in the case of divorce, but the decision was not approved by US occupation administrator Paul Bremer and did not take effect.
The proposal contained "articles that suppress social development and the progress of women", said female Shia council member Raja al-Khuzaai.
But SCIRI's al-Ubaidi disagreed, arguing it was important to be ruled under the same Islamic principles rather than by a secular civil code.
'Not over yet'
"We will not let this issue drop," she declared. "We will ask the governing council to reconsider."
Some Iraqi women are sceptical
about seeing improvements
Since 1991, Saddam Hussein's former regime had made some changes to the code to bring it more in line with Muslim laws, but its essence remained the same.
On the question of female-representation in the transitional Iraqi government that will take power from the US-led occupying forces after 30 June, it appeared unlikely the women's 40% demand would be met.
Al-Khuzaai, who called for the family law proposal to be repealed on Friday, said 30% was a more realistic target although some male members were against setting a fixed figure.
The rights of women - who make up more than half of Iraq's population - along with federalism and Islamic law are the main stumbling blocks for the Governing Council to negotiate before completing the temporary law, which is aimed at seeing Iraq through a period of transition.
Many women in Baghdad, however, appeared resigned to a life with fewer rights than men, as was the case before and during Saddam's time.
"We have never had rights, not now and not under Saddam," said Dania Idwa, 24, a student in the capital. "I have heard about the work women's groups are doing but I do not see any real improvements."