Family doctors are under intense pressure and general practice is running on empty, warns the Royal College of GPs (RCGP).
It says severe staff shortages are causing "unacceptable" delays for patients in England.
In a letter to Health Secretary Matt Hancock, its chairman says ministers must take urgent action to deal with the lack of GPs.
The government said it had recruited a "record number" of GP trainees.
Ministers are committed to recruiting 6,000 more GPs in England by 2025.
Prof Martin Marshall, who took over as RCGP chairman in November, says GPs are struggling with an escalating workload, which is causing many to burn out and leave the profession.
He says the problem is compounded by difficulty recruiting GPs and other members of staff to manage the demand.
A spokesperson from the Department of Health and Social Care told the BBC the recruitment of thousands more highly-skilled practitioners would mean patients would get "an extra 50 million appointments a year within the next five years."
Dr Andrew Dharman, who works at the The Avenue surgery in Ealing, said the stress has got worse because of the enormous workload placed on GPs.
He said: "Sometimes it feels like you're drowning. You know you're trying to stay afloat and on top of all the workload. And you're trying to make sure you're providing the kind of care that you envisage when you go to medical school.
"You feel frustrated sometimes that you can't necessarily do that because of the amount of work and patients."
Prof Marshall has asked Mr Hancock to clarify how he will increase the number of family doctors, and what significant investments he will make in the profession.
There are concerns that targets for extra GPs might not be met, with figures showing the numbers of doctors falling.
In the letter, Prof Marshall says: "No patient should have to wait three weeks for a GP appointment. This is unacceptable and our patients, and GPs, deserve better.
"We want a commitment to increase GP training places to 4,000 in 2020-21, as outlined in your election manifesto, but also to 5,000 soon after; and significant investment into initiatives to improve GP workload and retain existing GPs in the profession to improve the wellbeing and moral of the whole practice team."
GPs in England:
- According to official figures, there were just over 28,000 fully qualified full-time equivalent GPs in England as of September 2019. This is a drop of 3.7% since September 2015.
- There were 160.8 million GP appointments in the 12 months to November 2019, with 41.9 million of those in the last three months, 450,000 more than in the same period a year earlier