British nurse Jacintha Saldanha is suspected of taking her own life after she took a prank call from 2Day FM hosts Mel Greig and Michael Christian, who pretended to be the Queen and Prince Charles asking for an update on the condition of Catherine, the Duchess of Cambridge.
Ms Saldanha put through the call to another nurse who gave extensive details about the duchess's health.
The pregnant wife of Prince William was in hospital receiving treatment for severe morning sickness.
The privacy breach caused a huge scandal and the two Australian broadcasters have faced a backlash in the media, particularly in Britain.
The pair were taken off air and were now receiving counselling.
They were expected to make a public statement about the scandal soon, Austereo spokeswoman Sandy Kaye told the news.com.au website.
"They want to express their remorse publicly and we are hopeful they'll be ready to do that soon.
"They are still being wrapped in cotton wool at the moment and we are very mindful of their situation."
Mr Key today told TVNZ's Breakfast he thought it "probably" made sense for the industry to have a look at what happened on radio.
But he said he would be surprised if prank calls could be stopped.
"I must admit when I heard the news on Saturday morning I felt quite sick, at one level. I also thought I wonder whether there's more to this, it felt a very extreme reaction, but who knows, and you feel enormously for that family. It's such an awful thing."