That would bring the number of US troops under the level of 138,000 for the first time since April 2004, a year after US-led forces first invaded the country.
"President [George W.] Bush has authorized an adjustment in US combat brigades in Iraq from 17 to 15," Rumsfeld said.
His remarks came just a day after British Prime Minister Tony Blair raised the prospects of beginning a British troop pulldown next year.
Blair, who was also on a suprise visit to troops ahead of Christmas, remarked that he was pleased to learn of their high regard for Iraqi forces.
"This is a very hopeful sign because obviously the whole purpose is to build up the capability of the armed forces and the police so we can then draw down our own forces," Blair said.
The prime minister refused to be drawn on a timetable, but Friday's first edition of British tabloid The Sun said the process would begin in May. London's The Times claimed 1,000 troops had already been pulled back from frontline duties as the first stage of withdrawal.
Rumsfeld visits Iraqi training camp in Jordan
Rumsfeld visited an anti-terrorist training center for Iraqis near the Jordanian capital on Friday during a quick two-hour stop before returning to Baghdad.
The defense secretary attended two demonstrations by Jordanian trainers at the King Abdullah II Special Operations Training Forces center, where they simulated the interception of a car by heavily armed anti-terrorist teams.
The center, located near Tabarbour northeast of Amman, serves as a training base for special forces, Jordanians, Iraqis as well as other Arabs and foreign nationals, and was set up many years ago by the late King Hussein.
© 2005 Agence France-Presse
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