Alex Salmond has said the sympathies of Holyrood were with the family of Moray woman Mandy Mathieson.
An ambulance technician's decision not to respond to a 999 call that she had taken ill nearby because he was on a break is being investigated.
Crew stationed 21 minutes away and an air ambulance answered the emergency. Ms Mathieson, 33, died.
The first minister told the Scottish Parliament the investigations would be thorough.
He said: "My sympathies and the sympathies of the whole chamber are with the relatives of the woman who has died."
Health Secretary Nicola Sturgeon has received a report on the incident from the Scottish Ambulance Service (SAS).
The Health Professions Council has been asked to investigate.
Mr Salmond said: "It is not appropriate for me to comment any further on the circumstances of a particular case, however tragic, when these investigations are under way.
"But be assured by this that investigations will be thorough."
He added that he would not want the incident to reflect on the parliament's admiration for the work of the SAS.
Ms Mathieson's death in Tomintoul last month and the investigation into the response to her family's 999 call was raised by MSP Rhoda Grant.