The seven-page directive, the paper said, appears to authorise specific operations in Iran, most likely to gather intelligence about the country’s nuclear programme or identify dissident groups that might be useful for a future military offensive.
According to the New York Times, the order also permits reconnaissance that could pave the way for possible military strikes in Iran if tensions over its nuclear ambitions escalate.
"The authorised activities could strain relationships with friendly governments like Saudi Arabia or Yemen — which might allow the operations but be loath to acknowledge their co-operation"
The New York Times
It said that officials said that though the administration of George Bush, the former US president, had approved some clandestine military activities far from designated war zones, the new order was intended to make such efforts more systematic and long term.
The paper said the order seeks to build networks that could "penetrate, disrupt, defeat or destroy" al-Qaeda and other "terror" groups.
It also seeks to "prepare the environment" for future attacks by US or local military forces.
But the order does not appear to authorise offensive strikes in any specific countries, the paper said.
In recent years the US has sought to break its dependence on the Central Intelligence Agency and other spy agencies for information in countries without a significant US troop presence, according to the New York Times.
It said Petraeus’s order is meant for small teams of US troops to fill intelligence gaps about terror organisations plotting attacks against Washington.
But some defence department officials, the paper said, worry that the expanded role carries risks.
"The authorised activities could strain relationships with friendly governments like Saudi Arabia or Yemen - which might allow the operations but be loath to acknowledge their co-operation - or incite the anger of hostile nations like Iran and Syria," the New York Times reported.
"Many in the military are also concerned that as US troops assume roles far from traditional combat, they would be at risk of being treated as spies if captured and denied the Geneva Convention protections afforded military detainees."
The paper said the precise operations that the directive authorises are unclear and that what the military has done to follow through on the order is not certain.
The paper did not name several government officials who described the impetus for the order saying the document is classified.
It said spokesmen for the White House and the Pentagon declined to comment on the signing of the order.