The handwritten note from Jacintha Saldanha was addressed to her managers at the private King Edward VII's Hospital in London, where Catherine was being treated for acute morning sickness in December, the Sunday Times newspaper reported.
In one of three letters she left behind, the Indian-born nurse wrote: "Please accept my apologies. I am truly sorry. Thank you for all your support.
"I hold the Radio Australians Mel Greig and Michael Christian responsible for this act. Please make them pay my mortgage. I am sorry. Jacintha."
At an initial hearing in December, the inquest into the 46-year-old's death heard that Saldanha was found hanged with a scarf from her wardrobe in staff accommodation near the hospital.
She also had marks on her wrist, and there were no suspicious circumstances over her death.
Saldanha had accepted the hoax call from the RJs pretending to be Queen Elizabeth II and William's father Prince Charles, before passing it onto a colleague who divulged details of Kate's morning sickness.
The broadcast of the call made global headlines and Saldanha was found hanged three days later, triggering a major backlash against the radio network and the hosts.
The Sunday Times said that in another of the suicide notes, the nurse said she did not blame her colleagues for the distress that drove her to kill herself.
The other reportedly contained instructions for her funeral, which took place in India.
The inquest was due to resume on Thursday but media reports said it may be delayed.