"If you wanted an example of why the [U.S.-Afghan] security agreement should be signed soon, there's one," Hagel was quoted as saying by Military.com.
The unconfirmed reports suggested that the Afghan military was coordinating with Helmand province officials to give checkpoint authority to the Taliban.
The security agreement would outline how U.S. military forces would be engaged in Afghanistan beyond 2014, when international combat obligations are scheduled to diminish. Without the deal, the U.S. government said it might pull out of the country altogether, leaving the Afghan military to fend for itself.
The Loya Jirga, a tribal council, announced its support for the bilateral security agreement in November.
The U.S. government has pressed for a resolution by year's end to coordinate its mission with NATO allies.
The Afghan government said it may wait until 2014 elections to ratify the agreement.