"During the search operation ... a clash took place with Taliban," Abdul Jabar Salehthe, the deputy police chief of the northwestern province of Badghis, told the AFP news agency.
"Then aircraft mistakenly bombed the Afghan and Nato defence lines."
It was not immediately clear how many of the casualties were Afghan and how many from the international forces.
Nato search
The Nato-led International Security Assistance Force (Isaf) confirmed that the 25 soldiers were injured in an operation to recover the two missing colleagues, but it did not mention the air raid or discuss the condition of the paratroopers.
"The wounded service members were initially treated on the scene and subsequently flown to an Isaf medical facility for further treatment," a statement quoted US Navy Captain Jane Campbell as saying.
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"We are committed to taking every measure possible to rescue or recover our missing service members. We continue to do everything we can to find them"
US Navy Captain Jane Campbell, Nato spokeswoman
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"We are committed to taking every measure possible to rescue or recover our missing service members. We continue to do everything we can to find them."
Military sources have indicated that the missing men were not believed to have been captured by Taliban fighters.
Salehthe said that the paratroopers had drowned while trying to recover airdropped food packages from a river and the search for their bodies was continuing on Saturday.
The Taliban said that international forces had played down the actual toll from the air raid.
"There was ... a firefight between Taliban and Afghan and foreign forces in Murghab district of Badghis province. The fighting lasted for hours and was very intense, at a close distance," Qari Yusuf Ahmadi, a Taliban spokesman, said.
"By the end of the day, foreign forces bombed the area where the clash was going on and due to their own bombing, 32 foreign and 43 Afghan soldiers were killed."
Badghis is one of several provinces in the previously quiet west and north of Afghanistan, where Taliban activity has increased dramatically in recent months.