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 airstrike.
Separately in the south, a suicide bomber on a motorcycle detonated his explosives near a NATO military convoy in the province of Zabul, killing a man and a woman and wounding another three passers-by, the province's governor said.
Gulab Shah Ali Khail said the bomber struck in the district of Shajoy. Afghan Army officer Aimal Khan also said the motorcycle bomber killed two and wounded three.
Tech. Sgt. Angela Eggman, a NATO spokeswoman, confirmed that a military convoy had been hit by an explosion in Zabul that had wounded both Afghan locals and international troops. She did not have any further details.