Sydney 2Day FM presenters Mel Greig and Michael Christian have been taken off air after the call to London's King Edward VII Hospital was linked to the death of respected nurse and mother Jacintha Saldanha, 46, on Friday.
Police said there were no suspicious circumstances surrounding Ms Saldanha's death and it's believed she took her life.
The hosts had rung pretending to be the Queen and Prince Charles inquiring after the health of the Duchess of Cambridge who had been admitted with acute morning sickness.
Mr Kennett, the chairman of the national depression initiative beyondblue, said on Saturday he hoped the Australian public would support the two radio hosts involved in the prank.
"When they did this they had no intention to cause harm, it was a harmless prank.
"Now they will be under extraordinary pressure and I just hope that they get our support and that their employer provides them with the professional support to help them get through what will be a terrible few weeks," Mr Kennett told ABC radio.
NSW Premier Barry O'Farrell told reporters the two radio hosts must be feeling "terrible".
"I don't imagine in any way that those who were engaged in the typical FM radio stunt would have thought it would lead to this.
"I think there are some people today who are suffering, not just the family of the nurse but those who in some way were involved with what appears to be the trigger for this tragedy," Mr O'Farrell said.
* Readers seeking support and information about suicide prevention can contact Lifeline on 13 11 14 or Suicide Call Back Service on 1300 659 467.