The trust said it has taken additional measures to ensure it can continue to deliver a service to the public.
Head of service at the trust, Stephen Sheldon, said the public can help by only calling 999 in the event of a life-threatening emergency.
“That’s a cardiac arrest, chest pain or breathing difficulties, loss of consciousness, choking, or catastrophic bleeding,” Mr Sheldon added.
The service is advising the public to visit the NHS 111 Wales website for health advice or to consult a GP, pharmacist, and minor injuries unit.
The service describes the situation as “very rare”.
A critical incident was also declared in December 2020, due to high demand, particularly in south east Wales.
But an extraordinary incident was declared in 2023 after an ambulance spent more than 28 hours outside a hospital.
The Welsh Ambulance Service said 16 ambulances had waited outside the emergency department at Morriston Hospital, Swansea, at one time.
