Patients in Norfolk are being asked to book appointments and pick up routine prescriptions during the week to ease the pressure on the Saturday service.
Anglian Medical Care (AMC), which handles weekend queries, is now taking up to 200 calls hourly on Saturday mornings.
Lyn Reynolds, with AMC, said the number of calls had led to some delays.
She said people were trying to ring their surgery with general queries, not realising they were no longer open.
She said the staff were taking so much time to explain to non-emergency callers they should ring back during the week that urgent calls were being affected.
Under the new GP contract, which began in July, the duty of responding to unscheduled medical care was given to AMC, based in Hellesdon.
That month, more than 28,000 calls were received. More than 13,000 of the callers were put in contact with a GP or emergency practitioner.