The hotel manager told officers they were concerned for the welfare of a guest, Associated Press reported.
Police were called to the hotel at 5.04pm local time (9.04pm UK) and Payne was pronounced dead at 5.11pm.
Local media in Argentina subsequently reported that drugs and paraphernalia were found in Payne’s room, along with damage to furniture and a television.
Alberto Crescenti, a spokesman for the city’s ambulance service, said: “Unfortunately the injuries he had suffered as a result of the fall proved to be fatal. There was no possibility of resuscitating him.”
Meanwhile, the American gossip website TMZ was heavily criticised for publishing images that purportedly showed Payne’s body following the fall. The photographs have since been removed.
His death will be devastating for the legions of fans of One Direction (many of whom, seen below, gathered outside the hotel), who were for a period the biggest pop band in the world.
One Direction – often shortened to 1D – was propelled to success on the television show The X Factor in 2010 and went on to have a string of huge hits worldwide and five chart-topping albums before splitting up in 2016.