The constitution would be written by the US-appointed governing council which critics accuse of being unrepresentative American lackeys.
Secretary of State Colin Powell told The New York Times on Friday: "We would like to put a deadline on them - they've got six months. It'll be a difficult deadline to meet, but we've got to get them going."
He also raised the possibility that Iraqis themselves could set a timetable in the near future, adding that he has asked Iraqi leaders to estimate how long it would take to write a constitution and conduct elections.
"Now, if they take forever to give us the answer to that question, then we've got a problem," Powell said. "But I think they'll give us an answer fairly quickly."
Powell's comments come as the US is attempting to force through a new UN resolution to muster international help to stabilise post-war Iraq.
They also come as the UN's annual General Assembly is under way amid widespread doubts about the world body's future role in Iraq.
The administration of US President George Bush is at loggerheads with France, Germany and Russia - who opposed the Iraqi war - over a timeline for the transfer of Iraqi sovereignty.
Powell said the constitution drafted by Iraqi leaders would spell out whether Iraq should be governed by a presidential or parliamentary system, and clear the way for elections and the installation of a new government in 2004.
Not until then, Powell stressed, would the United States transfer authority from the US-led occupation to Iraq itself.