An ambulance service has warned that people may be asked to make their own way to hospital so it can protect its "precious resources".
The warning from the Welsh Ambulance Service comes amid a growing crisis across the NHS, including ambulance waits and packed hospitals.
Figures this week showed that around one in seven ambulance patients in England are still waiting more than an hour to be handed to A&E teams at hospitals, with nearly one in three waiting at least 30 minutes - higher numbers than at any point last winter.
Hospital waiting lists have hit a record high, while A&E departments experienced their worst performance on record, with data showing just 68.9% of patients in England were seen within four hours last month - the worst performance on record.
In a tweet posted on its account, the Welsh Ambulance Service told people that they may have to make their own way to hospital.
It wrote: "We are exceptionally busy at the moment. If your emergency is not life-threatening you may be asked to make your own way to hospital. We must protect our precious resources for those that need it most.
The average response time in November for ambulances in England outside London dealing with the most urgent incidents was nine minutes and 26 seconds, according to data, down from nine minutes and 56 seconds in October. The target is seven minutes. Data for London is not available.
The NHS also saw its highest number of ambulance callouts for serious illness for any November on record, while A&E dealt with more attendances than any previous November.
Ambulance workers in England and Wales are due to take industrial action on 21 December, while nursing staff are due to take action in England, Wales and Northern Ireland on 15 and 20 December.
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Health experts said delays show the NHS is facing "the toughest pressures since modern records began".
Danielle Jefferies, of health charity The King’s Fund, said: "Improving ambulance delays has been a government priority for some time, but today’s numbers show that one in seven ambulances are delayed by more than an hour as they wait for stretched A&E teams to assess patients.
Sarah Scobie, deputy director of research at the independent health think tank The Nuffield Trust, said: "NHS hospitals are desperately struggling to get patients in and patients out fast enough, and the situation continues to deteriorate as the temperature drops and we head into the most challenging winter months.
"Data shows the severe impact on staff with these delays, resulting in the loss of an average of 3,400 hours of ambulance staff time per day which could be used for patient care.
"Ambulances are one of the most visible and vital cogs of the emergency care machine, and it is becoming more painfully visible that they are under severe strain. The Government has confirmed additional funding to tackle the delayed discharges behind some of these problems, but it is far too late in the day to have a meaningful impact this winter.
"On top of confirmed ambulance and nurse strikes, unfortunately winter will keep getting harder for patients and NHS staff.”