Facebook Inc. reversed a decision to delete posts containing a famous Vietnam War photo of a girl fleeing napalm bombs after the move drew rebuke from Norway’s prime minister and the nation’s largest newspaper. The flare-up highlighted Facebook’s powerful role as a host for news—even though it says it isn’t a media company.

In a letter on its front page, Norwegian daily Aftenposten lashed out at Facebook Chief Executive Mark Zuckerberg for “limiting freedom” after the social network removed the image of the naked girl from...