Some listeners applauded the prank, like one who identified himself as Guido on the station's Facebook page and wrote, "It is only a joke people! it was great i love it!!!"
Others were outraged, with such negative comments outnumbering positive ones on 2DayFM's Facebook page before the nurse's death.
"Your stunt was done at a time in this country where there is paranoia about the intrusion of the media into people's lives," Gary Slenders wrote. "I know you will say it is harmless fun, the management of 2DayFM will say that it won't happen again, but this is exactly where the phone hacking scandal started."
The outcry grew exponentially after the hospital confirmed Saldanha's death, leading the Coles supermarket chain to remove all its advertising from 2DayFM.
"This death is on your conscience," reads one Facebook post. Several accused the two of having "blood on your hands."
Saldanha's family released a statement asking for privacy and directing questions to police. She is survived by her husband and two children.
"We as a family are deeply saddened by the loss of our beloved Jacintha," said the statement, released by police.
Saldanha worked at the King Edward VII Hospital for more than four years, and she was described as an "excellent nurse," well-respected by coworkers, the hospital statement said.
The hospital "had been supporting her throughout this difficult time," it said.
A St. James's Palace spokesman said: "The Duke and Duchess of Cambridge are deeply saddened to learn of the death.
"Their Royal Highnesses were looked after so wonderfully well at all times by everybody at King Edward VII Hospital, and their thoughts and prayers are with Jacintha Saldanha's family, friends and colleagues at this very sad time."
Separately, a palace spokesman told CNN: "At no point did the palace complain to the hospital about the incident. On the contrary, we offered our full and heartfelt support to the nurses involved and hospital staff at all times."
The hospital said Wednesday that it deeply regretted the call had been put through.