"I think for the next force rotation, we'll start seeing that (the) force rotation coming in will be smaller than the force that's in there," General Richard Cody, the US army's vice chief of staff, said.
"I know you're all waiting for a number here, and I'm not going to give you one because I don't know," Cody added in an interview with defence reporters.
The annual US force rotation for Operation Iraqi Freedom 3 is already beginning, and Cody said troops sent into the rotation in the coming year are likely to be smaller in number than the soldiers coming out of the country.
There are 150,000 American troops in Iraq - most of them army soldiers - but the number will go down to 138,000 before the end of this month.
The force was increased by 12,000 in December to provide security for the Iraqi elections in January.
US defence officials have said the number will likely begin falling below 138,000 as the Iraqi army and security forces are trained to take over security in the country.
Cody's comments came as Italian Prime Minister Silvio Berlusconi was accused in his country on Thursday of bowing to pressure from Washington after he apparently backtracked on an announcement that Italian troops would start withdrawing from Iraq in September.
Berlusconi has backtracked on an
earlier pledge to pull out troops
Berlusconi said on a television talk show this week that he wanted to begin reducing Italy's 3000-strong contingent in
September, but he later said he never set a fixed date for any pullout.
Italy has the fourth-largest foreign contingent in Iraq after the US, British and South Korean forces and any eventual withdrawal before other main partners would leave a hole in Iraq's international security network.
British Prime Minister Tony Blair said Wednesday he would not set any timetable for withdrawal of British troops.
Nato newcomer Bulgaria said on Thursday it would reduce the number of its troops in Iraq by around a quarter in June and decide this month whether to pull out completely by the end of the year.
The presence of Bulgarian troops
in Iraq is domestically unpopular
The Balkan US ally has sent 450 infantrymen to Iraq but its centrist government has been under pressure to bring them home from the unpopular mission in the run-up to summer general elections.
"There is a significant decrease of around 100 troops in the fifth contingent in Iraq," Defence Minister Nikolai Svinarov said.
Svinarov said the government, led by former king Simeon Saxe-Coburg, would decide by the end of the month whether to withdraw all troops by the end of 2005.
"There is no decision yet, but we have prepared a report," he said. "It is normal (to think) that if there is a presence in Iraq in 2006, it should be different from a military one."
Eight Bulgarians were killed In Iraq since the start of the war, and last week's shooting of a junior sergeant by US forces triggered calls from opposition parties for the country to set a timetable to pull out.