Speaking Friday, in the former Iraqi insurgent stronghold of Fallujah, Mr. Rumsfeld said President Bush has authorized the troop level to fall below the current baseline of 138,000.
He said the number of combat brigades would fall from 17 to 15. U.S. defense officials say about seven-thousand combat troops will be cut.
In other developments, a spokesman for Sudan's Foreign Ministry told Al-Jazeera television that six Sudanese men, including a diplomat, have been kidnapped in Iraq. Further details were not immediately available.
Meanwhile, thousands of Sunni Arabs in Baghdad, Tikrit and Mosul protested what they said were flawed December 15 parliamentary elections. Preliminary results show a strong lead for the main Shi'ite coalition.
Elsewhere, insurgents ambushed an Iraqi checkpoint in Adhaim, about 70 kilometers north of Baghdad, killing at least eight Iraqi soldiers and wounding about 20.
A suicide bomber also killed at least three people at a Shi'ite mosque in Balad Ruz, about 75 kilometers northeast of Baghdad.