Officials indicated it was unlikely the two missing had been taken captive.
NATO forces headquarters in Afghanistan said the two paratroopers from the 4th Brigade Combat Team, 82nd Airborne Division, went missing on Wednesday.
During the search operation to locate them, more than 25 NATO and Afghan national security forces members were wounded while fighting insurgents, said Lt. Col. Todd Breasseale, a NATO spokesman.
He could not say how many of the wounded were Afghan and how many were NATO, nor was the nationality of the NATO soldiers released.
The wounded were being treated in a coalition forces facility in Afghanistan, the alliance said in a statement.
Local police said the two were Americans who were swept away by a river in the western province of Badghis.
NATO did not specify where the incident took place, or provide any details of the mission.
Military officials, who spoke on condition of anonymity due to command policy, indicated that they did not suspect the case was similar to that of an American soldier who was captured by insurgents in eastern Afghanistan on June 30.
"We continue exhaustive search and rescue operations to locate our missing service members," spokeswoman Navy Capt. Jane Campbell said in the NATO statement. "We are doing everything we can to find them."
Western regional police Chief Gen. Ikram Uddin Yawar said two American soldiers were swept away by a river while trying to save two boxes that had fallen into the water while being airdropped during a resupply mission in the Bala Murghab district of Badghis province.
The deputy police chief of Badghis province, Abdul Jabar, said a helicopter had airdropped food parcels at a coalition base, but that strong winds had blown one box into the river and that two soldiers had been swept away by strong currents while trying to recoup the parcel. He said Afghan police had been helping coalition forces in the search Thursday and Friday but had been unable to find the two soldiers.
NATO could not confirm whether the missing paratroopers had been swept away by a river, and said it could release no further details.
The soldier who disappeared on June 30 near Afghanistan's border with Pakistan has still not been found. He was shown as a Taliban captive in a propaganda video in July. U.S. military officials have said little about the search for 23-year-old Pfc. Bowe R. Bergdahl for safety reasons, and it is unclear whether he is being held in Afghanistan or Pakistan.
Separately Friday, NATO said two American service members were killed Thursday by a roadside bomb in southern Afghanistan. The statement gave no further details.
The deaths bring to three the number of U.S. service members killed in the Afghan war so far this month. October was the deadliest month of the eight-year war for U.S. forces with 59 deaths reported.
Associated Press writers Deb Riechmann and Elena Becatoros in Kabul contributed to this report.