Syria called the helicopter-borne assault, which unnamed officials have said targeted an Iraqi smuggling fighters across the border, a "criminal and terrorist aggression".
At least eight people were reportedly killed in the raid.
The order identified 15 to 20 countries, including Syria, Pakistan, Yemen, Saudi Arabia and other Gulf states where al-Qaeda fighters were believed to be operating or hiding, a senior administration official told the newspaper.
Despite the order, each mission required approval from senior Bush administration officials, the report said.
Under the authority, a US Navy special forces team raided a suspected a compound in the Bajaur region of Pakistan in 2006, the paper said, citing a former top CIA official.
Military planners watched the raid "live" at CIA headquarters in Virginia through a video camera on a Predator drone aircraft that was sent to the area, it said.
Officials said the list of targets did not include Iran, but said that that US forces had carried out reconnaissance missions in Iran using other classified orders, the paper reported.
About one dozen additional operations have been cancelled in the past four years because they were deemed too risky, too diplomatically explosive or relied on insufficient evidence, the paper said.
The Pentagon would not comment on the specifics of the report but acknowledged that the US military seeks to capture or kill al-Qaeda fighters and other targets wherever they are.
"We work with partners around the world to identify, seek, capture, kill if necessary, terrorists and their networks, where they plan their operations, where they conduct their operations, where they seek safe harbour," Bryan Whitman, a Pentagon spokesman, said.