Paul Bremer on Monday said the current draft of the constitution would make Islam the state religion of Iraq and "a source of inspiration for the law" - as opposed to the main source.
Many Iraqi women have expressed fears that the rights they hold under Iraq's longtime secular system would be rolled back in the interim constitution being written by US-picked Iraqi leaders and their advisers, many of them Americans.
US lawmakers have urged the White House to prevent Islamic restrictions on Iraqi women.
Asked what would happen if Iraqi leaders wrote into the constitution that Sharia (Islamic law) is the principal basis of the law, Bremer suggested he would wield his veto. "Our position is clear. It can't be law until I sign it."
Bremer must sign into law all measures passed by the 25-member council, including the interim constitution. Iraq's powerful Shia clergy, however, has demanded the document be approved by an elected legislature.
Under US plans, a permanent constitution would not be drawn up and voted on until 2005.
Bremer used the inauguration ceremony at a women's centre in the southern city of Karbala to argue for more than "token" women's representation in the transitional government due to take power on 30 June.
Women's rights are to be
enshrined in future constitution
"I think it is very important that women be represented in all the political bodies," Bremer said.
"Women are the majority in this country, in this area probably a substantial majority," he said, referring to the Saddam Hussein's alleged 1991 purges of Shia Muslim men. Those killings left the holy city of Karbala and other Shia cities dotted with mass graves and brimming with thousands of widows.
Enshrining women's rights in a future constitution could be difficult.
US observers have predicted liberal reforms introduced in the transitional law could well be rolled back in a future constitution. Bremer acknowledged that US influence on an Iraqi constitution would fade after the 30 June handover.
Muhsin Abd al-Hamid, the current council president and a member of a committee drafting the interim constitution, has proposed making Sharia the "principal basis" of legislation
"There will be a sovereign government here in June. The Iraqis then will then have responsibility for their own country," Bremer said.
There are three women on the Governing Council.
Muhsin Abd al-Hamid, the current council president and a member of a committee drafting the interim constitution, has proposed making Sharia the "principal basis" of legislation.
The phrasing could have broad effects on secular Iraq. In particular, it would likely moot much of Iraq's 1959 Law of Personal Status, which grants uniform rights to husband and wife to divorce and inheritance, and governs related issues like child support.
In December, the council passed a decision abolishing the 1959 law and allowing each of the main religious groups to apply its own tradition - including Islamic law. Bremer has not signed it into law.