Edinburgh Central MSP Ms Davidson called for at least 10 per cent of all health cash to be directed to GPs by 2020.
She was speaking at the Southside Surgery in Newington, which is being run by NHS bosses after repeated efforts to recruit two new GP partners failed.
A letter sent to patients by the remaining GPs, Dr Eileen Sanderson and Dr Alyson Reive, last month said the surgery building will have to be sold by next summer – as it is part-owned by two GPs who have retired – and its 5400 patients could be sent to other practices if a suitable site cannot be found.
The letter said: “Options are however very limited and if (as is likely), no other location can be found, then Lothian Health Board plan to close the practice entirely and disperse our patients to other surgeries in the area.”
NHS Lothian insisted then that it has no plans to close the surgery and it is confident it will find new premises in time.
Southside Surgery is the sixth practice to be taken over by NHS Lothian in recent months, after Bangholm, Kirkliston, Leith Links, Polwarth and Eskbridge Medical Practice in Musselburgh, were struggling to cope.
Bangholm and Kirkliston have since returned to independent practice.
Ms Davidson said: “We need to have a long-term plan for looking after GP services.
“90 per cent of people’s contact in terms of health is through general practice but it gets less than 7 per cent of the NHS budget in Scotland.
“The Royal College says that’s got to change and we support their plans to increase the money within the health budget that’s directed to general practice because it saves money down the line.”
She added: “GP surgeries in all parts of the country are just swamped under the weight and they cannot cope.
“Doctors are telling us they cannot cope, patients are telling us they can’t get on a list and they can’t get an appointment.
“Something has got to give, so we have got to get a really strategic look at how we support this.”
Conservative health spokesman Donald Cameron said: “We are facing a GP crisis right across Scotland and it is time the SNP acted.
“Extra funding for general practice would help us deliver a better local service for people right across Scotland, so you can actually get an appointment when you need it, instead of waiting at the end of a phone line.”
Dr Alan McDevitt, chair of the BMA’s Scottish GP Committee, said: “It is essential that general practice receives extra funding and resources to ensure that it can provide the care that our patients deserve.
“The health service in Scotland is facing unprecedented pressures, with increasing demands on the NHS outstripping resources and significant problems in recruiting and retaining medical staff.”