Patients who try to make an appointment at their GP in person have been warned they could be turned away.
A clinic in Edinburgh has informed its 6,000 patients it will be moving to a telephone assessment system three days a week.
Read more: Record number of GP surgeries taken over by health boards
The Links Medical Centre said: "Patients requiring to be seen by a GP should no longer come to the surgery on a Monday, Wednesday or Friday morning, but should telephone the surgery on the usual number at 8am and they will be appointed to the triage list.
"Unfortunately, we do not have the facilities for the number of patients who would usually come to the urgent problem clinic to wait in the surgery for a call back. This is due to overcrowding and confidentiality issues.
"We would ask that you only attend if you feel your problem is urgent. Patients requiring to be seen routinely may be advised to return home and await a call from the triaging team."
The move comes amidst growing fears over a lack of GPs at surgeries across Scotland with estimates suggesting a shortfall of some 800 by 2021.
Miles Briggs, health spokesman for the Scottish Conservative Party, said: "Every week it seems the SNP's GP crisis hits a new low.
"A situation where patients are being sent packing is dangerous and could put lives at risk."
Read more: Two thirds of Scottish doctors work part-time
Andrew Buist, of the British Medical Association's Scottish GP committee, said surgeries somehow had to take steps to ensure they were able to deal "effectively" with patients and "protect patient confidentiality".
The Links surgery was taken over by NHS Lothian which works with Edinburgh Integration Joint Board (EIJB) in 2015 after it failed to replace three doctors and was forced to drop 2,000 patients.
An EIJB spokesman said: "The Links Medical Centre has opted to introduce the triage system to allow its GPs to deal with patients more efficiently and effectively.
"Anyone who presents at the practice with an urgent medical issue will be seen by a GP."
A Scottish Government spokesman said: "Patients seeing the most appropriate healthcare professional first is in line with the new GP contract agreed with the BMA."
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