Immigration and Customs Administration agents may have to atone for their sins ... after one agent was caught on video shooting a priest in the head with a pepper ball during an ICE protest -- but the feds say the footage doesn't show the full story.

The icy confrontation between federal agents and protesters went down at an ICE detention facility in Broadview, Illinois on September 19 ... but the video is only now making the rounds.

Watch the clip ... you can see Reverend David Black on the sidewalk, pleading with arms open toward three agents in combat gear standing on the roof ... The agents start firing pepper balls at the crowd during the demonstration -- one of many over the past weeks protesting the detention and deportation of undocumented immigrants. Kelly Hayes via Story

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