The two paratroopers, from the 4th Brigade Combat Team, 82nd Airborne Division, disappeared in Badghis province, a remote area that borders Turkmenistan, on Nov. 4. Local police had said the two had been swept away by the river as they tried to recover the supplies.
Afghan and international forces are still searching for the second soldier, NATO said in a statement.
During the first days of the search, intense fighting broke out with militants in the area. Eight Afghans - four soldiers, three policemen and an interpreter - were killed, while 17 Afghan troops and five American soldiers were wounded.
Afghanistan's Defense Ministry had said at the time that the deaths and injuries likely happened "during an air attack by NATO forces" during the fighting.
NATO has said authorities are investigating whether some of the casualties were caused by a friendly fire air strike.