The statement came shortly after the key army division was told it would stay in Iraq for an indefinite period of time amid fears of increased resistance operations.
The Pentagon deployed about 16,500 soldiers from the division during the war, and about 15,000 remain in Iraq and Kuwait.
Some 146,000 US troops are still in Iraq, according to a senior defence official in Washington.
On Monday, officials at the Army’s Fort Stewart in Georgia said plans for the entire division to return by September had been put on hold.
They also said that around 9,000 soldiers, including troops from the 1st Brigade Combat Team and 2nd Brigade Combat Team would stay indefinitely.
“The process in sending units home is … not on a timeline,” an official said.
But the senior defence official said on Tuesday that US Secretary of Defence Donald Rumsfeld was committed to bring the entire division back home this autumn.
“This fall, they’ll be coming home. That stands,” the official said.
The official refused to give a specific time, saying “the planning’s not that finite and I don’t want to be yo-yo-ing these guys around”.
Uncertainty over the return of the 3rd Infantry Division troops has caused frustration among the families of the soldiers.
The division was the first to enter Baghdad during the war and has assumed a major role in the post-war occupation of Iraq.
Thirty-seven of the division’s soldiers have been killed in the country, including one who died Monday.
Meanwhile, US top occupation administrator, Paul Bremer, said on Tuesday that US-led forces would not stay in the country longer than necessary.
He claimed that “our time here is in the hands of the Iraqi people”.
The first priority, Bremer said, was to draft a constitution to pave the way for elections, which are not expected to be held before June 2004 at the earliest.
French President Jaques Chirac said on Tuesday that Paris could not consider sending troops to Iraq under existing conditions.
Deploying troops to Iraq “is not conceivable within the current framework”, Chirac’s spokeswoman, Catherine Colonna quoted him as saying during talks with visiting Czech President Vaclav Klaus.
Last week, Foreign Minister Dominique de Villepin said France would only join a multinational force in Iraq if it were formed under a UN mandate.
But Croatia’s defence ministry said Zagreb was planning to send some 60 special forces soldiers to operate under US command.