St John Ambulance says it has been trialling a new way of prioritising 111 calls following criticism of its response in two emergencies where people died.
Coroners' reports into the deaths of a 28-year-old mother soon after she gave birth, and a nine-year-old girl in a crash, have highlighted problems with the service.
Taufau Laloava died of a septic infection three weeks after giving birth in Auckand in 2013.
Her partner had called 111 twice in 22 minutes but was told the case was non-critical and that the ambulance was busy.
Coroner Katherine Greig recommended St John review the questions used by 111 call-takers to prioritise patients.
A second coroner's report, on the death of nine-year-old Lydia Milbank, found failures by St John staff who attended her after she was hit by a motorbike near Lake Rotoma in 2014.
The reported failures included a delay in getting her to hospital, as well as a faulty diagnosis.
Lydia's mother, Janet Milbank, said she would like to see greater support given to St John, including more ambulances and more staff.
"St John relies heavily on donations and, being an essential service, I believe the government should put more money towards providing better resources for them."
St John Medical Director Tony Smith said since Ms Laloava's death they had been trialling a system where a registered nurse calls back patients classified as non-urgent to more fully assess their condition.