In interviews on Australian television networks, presenters Mel Greig and Michael Christian insisted their prank call to the King Edward VII's Hospital in London was never meant to go so far and they had expected staff to hang up on them.
The pair posed as the Queen and the Prince of Wales when they rang the hospital where Kate was being treated for acute morning sickness.
Nurse Jacintha Saldanha took the initial call and, believing it to be genuine, put them through to another colleague who was duped into describing Kate's condition in detail.
A tearful Ms Greig, who was at times comforted by Mr Christian, said: "There's nothing that can make me feel worse than what I feel right now.
"And for what I feel for the family. We're so sorry this has happened to them."
Mr Christian said he was "gutted, shattered, heart-broken" by the nurse's death.
Mother-of-two Ms Saldanha, 46, was found dead on Friday in what appeared to be a suicide.
Ms Greig said: "I remember my first question was 'Was she a mother?'.
"I have thought about this a million times in my head, that I just wanted to reach out to them and just give them a big hug and say sorry."
Mr Christian, added: "I just hope they get the love, the support, the care they need."
In a second interview, the DJs said they had expected their fake call to last 30 seconds before they were cut off. Ms Greig said: "Not for a second did we expect to speak to anyone. We expected to be hung up on."
The pair said their greatest concern now was for the family of Ms Saldanha. Mr Christian added: "It was something that was just fun and light-hearted and a tragic turn of events no-one could have predicted or expected.
"We are shattered, heartbroken and our deepest sympathy goes to the family, friends and all those people affected. Mel and myself are incredibly sorry for what's happened."
Scotland Yard is understood to have asked police in Sydney for assistance, with a view to interviewing the two 2Day FM presenters ahead of an inquest into Ms Saldanha's death.
A post-mortem examination is due to be held this week and an inquest opened and adjourned at Westminster Coroner's Court, Scotland Yard said. The death is not being treated as suspicious.
Southern Cross Austereo chairman Max Moore-Wilton has said the board would consider its response to a letter from Lord Glenarthur, chairman of Edward VII's Hospital, in which he called for the "truly appalling" broadcast to "never be repeated".
Ms Greig and Mr Christian, who are on indefinite leave, are receiving "intensive psychological counselling" to deal with the tragedy, the Australian media firm said.
The Australian Communications and Media Authority, which regulates radio broadcasting, confirmed it had received complaints from around the world, and said it was considering whether it should launch an investigation.