Professor Helen Stokes-Lampard, chairwoman of the Royal College of General Practitioners, said most GPs were already working "at the limits of what is safe".
"Patients can always see a GP through the out-of-hours service when they urgently need one," she said.
"But there is a distinction between 'need' and 'want', and there is very little evidence to show that patients want or need to see a GP for non-urgent care on a Sunday afternoon."
Ms Stokes-Lampard said some GPs are already failing to keep pace with patient demand and stressed that "patient safety - and doctors' own health - must be paramount".
The Government has pledged to improve access to GPs in the evenings and at weekends.
But she told the Guardian that "it's unrealistic in the current climate. We haven't got the people, we haven't got the resources."
Instead, she urged the Government to invest in general practice so that GPs can provide a safe weekday service.
However, the Government has hit back, with a spokeswoman for the Department of Health saying: "This is a common-sense reform with wide public support - and one we will deliver."
She added: "People don't just get ill Monday to Friday, nine to five, and 18 million patients now have weekend and extended access to a GP, which has already shown evidence of relieving pressure on other parts of the NHS."
Some 1.3 million patient consultations take place in general practice every day, and Ms Stokes-Lampard estimated that there are around 60 million more every year compared to five years ago.
Last month, she warned that patients could be forced to wait up to four weeks to see a family doctor, which could expose them to "serious risk".
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