Mr Rumsfeld came directly from Afghanistan

Further reductions will be considered "at some point in 2006", he said.

The move will take the number of US soldiers to below the 138,000 level, seen for most of this year.

Two army brigades scheduled for deployment to Iraq - one currently in Kansas state, the other in Kuwait - will no longer go.

A brigade is usually made up of 4,000-5,000 troops.

Mr Rumsfeld said US commanders would "continue to shift their focus to emphasise training and supporting the Iraqi security forces".

Political process

Mr Rumsfeld has previously said that an extra 20,000 troops sent to Iraq to improve security during recent elections would be withdrawn in January, to bring US force levels back to the 138,000 baseline.

Now Mr Rumsfeld says troop numbers will dip below that level.

"The adjustment being announced today is a recognition of the Iraqi people's progress in assuming added responsibility for their country," he said.

Mr Rumsfeld is due to meet Iraqi President Jalal Talabani on Friday, after staying overnight in Iraq for the first time since the fall of Saddam Hussein.

After his arrival in Iraq, Mr Rumsfeld said Iraq would need time to build a working democratic government following elections on 15 December.

"The Iraqi people who are involved in this process are relatively new to the political process. It will take some time, I suspect," he said.

"It is a big, big, enormous thing for them to try to accomplish in a relatively short period of time."

More than 2,100 US troops have been killed in Iraq since the end of the invasion in April 2003, while Iraqi deaths are put at more than 30,000.