Update 9pm: Naas General Hospital has confirmed that its Emergency Department (ED) reopened at 9pm this evening, with the Department now receiving both walk-in attendances and ambulance admissions.
Update 8pm: Minister for Health Simon Harris has released a statement tonight.
"Like all of us, I was numb when I heard about this terrible tragedy. I visited the hospital this evening to extend my sympathies to the family on the death of their loved one.
"I also wanted to support the incredible efforts of the staff in Naas General Hospital on what was an extremely difficult and upsetting day and to convey my hope of a full recovery to the injured paramedic staff.
"The Director General of the HSE has briefed me on the situation and informed me that a number of investigations will now take place. My thoughts and prayers remain with the family of the deceased man and with the injured paramedics."
Dublin Midlands Hospital Group has also offered their condolences.
Dr Susan O’Reilly, Chief Executive, Dublin Midlands Hospital Group said:
“I wish to extend my sincere condolences on behalf of the Group to the family of the deceased. I also wish to acknowledge the two paramedics from the National Ambulance Service who, despite their injuries, responded heroically in the immediate aftermath of the incident. We understand that one of the paramedics has since been discharged from hospital; the other is under observation but is in a stable condition. We wish both a speedy recovery.
Update: 6.30pm Union representatives at Siptu have called for an immediate examination of the ambulance fleet following the patient's death.
Organiser Paul Bell said: "Firstly, we would like to express our deepest sympathy with the family of the patient who died and our grave concern for the two paramedics who tried in vain to save his life.
"This tragedy should never have happened."
Ambulances normally carry up to six sealed cylinders of different types of potentially flammable gas to treat patients at a scene and while transporting them.
They carry oxygen and also an analgesic gas and air mix for pain relief.
Michael Dixon, chair of the National Ambulance Service Representative Association (NASRA), offered condolences to those caught up in the incident.
"Our thoughts and prayers are with the man who lost his life in the back of the ambulance," he said.
"But we are also concerned for the two paramedics injured as well."
Update: 6.05pm HSE Chief Tony O'Brien has told reporters at Naas General Hospital that the engine does not appear to have been responsible for the blaze.
He said: "It does appear that the fire started towards the rear of the ambulance, in other words it does not appear that this was related to the engine.
"Without prejudicing that outcome, we are currently focusing our concerns, or our actions, on the possibility - and I stress the possibility - this was an oxygen-related incident.
"As a result, a safety action notice has been issued to all National Ambulance Service personnel in relation to that issue, in particular vigilance, as I want to stress in this case the staff did everything they possibly could."
Two paramedics were injured in the incident and one of the paramedics, in his 30s, was initially treated at the scene before being taken to the specialist burns unit in St James' Hospital in Dublin for treatment to severe injuries.
The second paramedic, also believed to be in his 30s, was treated in Naas but his injuries are believed to be minor.
Earlier: An elderly male patient has died after an ambulance burst into flames at Naas General Hospital in Co Kildare.
The fire happened at around 2pm at the entrance to the Emergency Department of the hospital.
A man who was in the ambulance at the time was pronounced dead at the scene.
A Garda spokesman said a medic was also injured and his condition is not believed to have been life-threatening.
Fire crews from Naas attended the scene.
Witness Rob Moore was inside the hospital when the fire alarm sounded and rushed out to see what was happening.
"I don't know what actually happened, but the whole thing just went up," he said.
"As I came out of the door of the hospital I could see two paramedics at the back (of the ambulance), one of them was really severely burnt.
"I think there was a fireman there, who was off-duty, he started to get things under control.
Scene at Naas General Hospital where a man has passed away following an ambulance catching fire. pic.twitter.com/LqgLdp3G8u— Robin Schiller (@11SchillRob) September 22, 2016
"Everyone was pulled away from it then."
Mr Moore said he did not hear an explosion but believed he heard a bang or a thud.
He also saw who he believed to be one of the paramedics being taken to an area outside the hospital, where medics stripped him down to treat his wounds.
Both the Gardaí in Naas and the HSE are investigating all of the circumstances surrounding the fire.
The area has been sealed off for a technical examination and the emergency department has been temporarily closed.
We are live at Naas Hospital following reports that a person has died after an ambulance caught fire. More on our news at 4pm. pic.twitter.com/9vmgc0L9ny— Kfm Radio (@kfmradio) September 22, 2016
The HSE confirmed that the Emergency Department has closed temporarily, while the hospital’s emergency plan was put into action, meaning all staff and patients have been evacuated.
Any members of the public seeking access should visit their GP first and if necessary attend another Emergency Department.
The HSE said: "The National Ambulance Service (NAS) has implemented appropriate diversion protocols and patients are being taken to alternative hospitals.
"The NAS has informed both the Health and Safety Authority (HSA) and An Garda Siochana and a full investigation is underway into the incident.
"The hospital has advised any member of the public seeking access to medical care to visit their GP in the first instance and if necessary to access another Emergency Department in an alternative hospital. The hospital has also requested that members of the public refrain from visiting at this time."
Louise O'Reilly, Sinn Féin spokeswoman on health, said the fire was "an unfortunate demonstration of the abdication of responsibility by the Health Minister and the Department (of Health) in ensuring that these services have the support and resources they need.
"The paramedics and personnel want to ensure quality of care and patient safety and this cannot happen without a commitment from the minister in terms of resourcing.
There is a need for (Health Minister) Simon Harris to make a statement on this and he must make himself available to discuss how he intends to fund these services in the budget."
The Health Service Executive had €7.5m to buy 47 new emergency ambulances last year.
Rules require any ambulance over seven years old to be replaced for safety reasons.