There is a 'significant risk' to patient safety if industrial action in the health service continues at the current rate.
The warning is issued in a statement released and signed by the Chief Executives of the five health trusts in Northern Ireland and Northern Ireland Ambulance Service.
Thousands of patients are facing postponed appointments and surgeries this week as hospital workers campaign for pay alignment with colleagues in the rest of the UK as well as better staffing levels.
Cancer diagnostic appointments are now included in those that have been postponed meaning cancer diagnosis could be delayed.
The Belfast Trust, the largest trust in the province and the trust which has cancelled the majority of appointments, has apologised blaming the industrial action.
The union UNISON said it asked the trust to exempt cancer services from industrial action.
Chief Executive of the Belfast Trust, Martin Dillon said, "My understanding is that my team did draws these issues to the union's attention on more than one occasion but were not able to secure the derogations.
"I do not wish to get into a 'he said, she said'. What I want our trade union colleagues to do now is to sit down with us and agree the appropriate derogations in the interests of these very vulnerable patients."
In a statement, the Chief Executives of the Belfast Trust, Northern Trust, Western Trust, Southern Trust, South Eastern Trust and NIAS said a solution was needed 'urgently'.
The statement reads, "We recognise the dedication and commitment of all our staff and also respect their right to take industrial action. However, the level of escalation, in what is only week two, is causing us real concern with regard to service continuity during what is already a very demanding period.
"We are all aware that Health and Social Care in Northern Ireland requires a long-term funding settlement that addresses service, workforce and pay pressures in a sustainable manner.
"We have been struggling with a system where funding has been made available on a yearly basis, which makes it impossible to plan for the long term. Demand is increasing and will continue to do so meaning that the current system is simply unsustainable.
It continued, "Given the immediate risk arising from the industrial action, it is essential that we find a means of resolving the dispute in the short term. We accept that this is not possible without ministerial intervention and further resource.
"We now all need to urgently find a resolution to the current dispute."
Patricia McKeown from UNISON said she cannot understand why the Belfast Trust has cancelled cancer diagnostic services.
"We challenged them (Belfast Trust) why they had cancelled cancer diagnostics, we do not understand the answer and we have asked them what action they are going to take," she said.
Ms McKeown said members of the union who guaranteed they would cover cancer services, were at work.
She added that she believes more money alone would solve the crisis.
Emergency services and day centres are not affected by the industrial action with all services due to resume as normal on Friday December 6.
For more information on cancellations and postponed services visit: