Adam Cairns, the Chief Executive of Cardiff and Vale University Health Board - which runs the University Hospital of Wales - spoke to ITV News this evening.
He told Jonathan Hill that the findings of the report by the Royal College of Surgeons are "troubling, worrying and unacceptable".
He said the primary problem - of getting patients into the hospital - caused cancellations of planned procedures, and needs to be tackled with a "much more resilient plan" in future.
Labour MP Ann Clwyd has called for an inquiry into failings at Wales' biggest hospital and called it the Welsh equivalent of the Mid-Staffordshire Hospital scandal, in an interview with the BBC.
Adam Cairns, the Chief Executive of Cardiff and Vale University Health Board, which runs the University Hospital of Wales, has told BBC Radio 4's World at One programme that 12 patients have died on the cardiac surgery waiting list over the last 15 months.
The Cardiff and Vale of Glamorgan Community Health Council says it wants to "provide some reassurances to patients who are currently or awaiting surgery within the University Hospital of Wales."
The report from the Royal College of Surgeons says that South Wales is the only part of the UK where patients are dying on cardiac surgery waiting lists.
Other problems identified included:
- Children being fitted with hearing aids because of a lack of time and resources to insert grommets to treat ear infections
- Patients "suffering complications" because of delays in treating kidney stones
- A&E and intensive care units being "frequently grid-locked" with patients "often stacked up in corridors and ambulances".
The Royal College of Surgeons sent its report to the health board, Health Inspectorate Wales, and the Welsh Government.
Wales' health minister, Mark Drakeford, was "very concerned" to read the report "and the risks to quality and safety it highlighted."
The Welsh Conservatives have reiterated their call for a major inquiry into the state of the NHS in Wales, similar to a high-profile one carried out in England.
Fourteen NHS trusts in England were investigated in an inquiry carried out by Professor Sir Bruce Keogh, England's NHS medical director, and a report published earlier this month.
It was set up following the Mid-Staffordshire Hospital scandal, where hundreds of patients died due to poor care.
Cardiff and Vale University Health Board says it has developed "a detailed action plan to make sure that we are addressing all areas" of concern, and the Royal College of Surgeons will visit again in September to see if there has been improvement.
The health board is looking at all options to increase cardiac surgery capacity, and looking at proposals to get patients treated more quickly.
Chief Executive Alun Cairns said the health board is working with surgeons "on a range of actions", and looking at what extra capacity could be provided, and improving how it manages emergency, care.
Wales' biggest hospital has been described as "dangerous", in a highly critical report from the Royal College of Surgeons.
It found that "patients are regularly dying on the waiting list from their cardiac pathology" and there was "universal consensus" among clinicians at the University Hospital of Wales in Cardiff that services there were "dangerous."
It warns "the current situation represents a severe risk to patients and urgent action is required."
"A wide range of concerns were raised" by clinical leads at the hospital during a routine visit by the RCS in April - the most prevalent was "the inability to admit patients for elective surgery." There were more than 2,000 operations either cancelled or not scheduled between January and March 2013.
"The main reason for this is the apparent unconstrained admission of emergency patients and the inability to effectively discharge patients", the report said.