The temporary measure was confirmed this week by NHS Fife as it revealed that A&E has recorded its highest ever numbers in recent months.
The region’s health authority is also trying to cope with staff absences as a result of the virus, and patients testing positive on admittance to wards.
The sustained pressure, which has already resulted in tighter restrictions on visitors to hospital wards, mirrors the picture across Scotland.
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NHS Borders has announced the cancellation of all routine operations for at least one week in a bid to manage the caseloads.
Hospitals across the Kingdom are described as “extremely busy” as a summer COVID spike starts to impact - with concerns of more problems to follow in the autumn and winter.
Andrew Mackay, deputy chief operating officer for acute services, said: “Our hospitals are extremely busy due to an increased demand for inpatient care for both COVID-related and non COVID-related conditions.
“The numbers of those in our care who have recently tested positive for the virus fluctuates as patients are admitted and discharged.
“However, the numbers have increased sharply in recent weeks.”
Mr Mackay said Fife’s hospitals were seeing “a considerable number of patients” admitted for other conditions who test positive for COVID-19 as part of the admission process - adding to the pressures on services at a time when rising numbers of staff were absent after also testing positive.
Clusters of the virus in individual bays and wards are reducing patient flow through hospitals - and it is taking longer to discharge people who are ready to go home.
He added: “While we have continued to deliver urgent surgical procedures and most of our non-urgent surgical programme, the increase in pressure in recent days has required us to temporarily postpone some elective procedures.”
On A&E, Mr Mackay said the frontline department “remains incredibly busy” with many of its highest attendances on record coming in the last few months.
He again appealed to people to use it responsibly.
“The Emergency Department is designed to care for those who have a life-threatening emergency - that is not new.
“Where a condition is less serious, we are asking people to use one of the range of alternatives available, which allows our clinicians to dedicate more time to those people who are most unwell, and who are most in need of their care and expertise.”