The ambulance service for the south west of England said it had recorded its busiest day on Sunday.
Staff responded - either in person or via the phone - to 3,522 cases in total, averaging two per minute.
A "perfect storm" of factors include the hot weather, tourists visiting the area, and a rise in coronavirus cases.
The South Western Ambulance Service NHS Trust said people should only call 999 in a genuine, life-threatening emergency.
"Our service is continuing to experience an unprecedented high level of demand, and we have just had two of our three busiest days in our history," Ceri Smart, the trust's director of operations, said.
"Our people are working incredibly hard, 24/7, to ensure we are there for the people across the South West who need us most."
SWAST also experienced its busiest week on record for the second time this month, responding to 23,088 incidents in the seven days prior to 18 July, which is equivalent to one case every 26 seconds.
Incident numbers were 30% higher than those recorded in the equivalent week two years ago.
The Trust said the situation had been made worse by people not knowing when it was appropriate to call 999, with many callers ringing back to check the ETA of an ambulance, or because they could not get through to the NHS 111 service.
South Western Ambulance Service NHS Trust covers the former Avon area, as well as Somerset, Wiltshire, Dorset, Gloucestershire, Devon and Cornwall.