Speaking to reporters in Kabul, Gen. David McKiernan said with violence up 30 percent in Afghanistan from last year, he needs more combat power and support elements, which could mean an additional 15,000 troops, the Voice of America reported.
His call for more troops would be over and above the several thousand announced by Bush last week, the report said.
McKiernan's comments came as U.S. Defense Secretary Robert Gates arrived in Kabul.
The general also issued new orders to avoid civilian casualties.
Currently, there are about 33,000 U.S. troops in Afghanistan.
McKiernan was quoted as saying senior Pentagon officials have confirmed the need, adding it was not a question of whether but when he will get the troops, which would depend on troop cuts in Iraq.
McKiernan also noted there can be no "right outcome in Afghanistan without some solution to the militant sanctuaries in the tribal areas in Pakistan."
He said while Pakistan has taken more action recently, it was too soon to make an assessment of the outcome.
Adm. Mike Mullen, chairman of the U.S. Joint Chiefs of Staff, arrived in Pakistan Tuesday to discuss the border security issue, the VOA report said.
Notable deaths of 2014 [PHOTOS]