Some GPs in England have been warned they could lose extra funding if they fail to meet their commitments to keeping surgeries open for longer.
The government wants surgeries to open between 08:00 and 20:00, seven days a week, unless they can prove the demand is not there.
It said many patients were going to under-pressure A&E departments because they could not get GP appointments.
The British Medical Association accused ministers of "scapegoating" doctors.
Surgeries are currently expected to open between the core hours of 08:00 and 18:30, Monday to Friday.
Extra funding is available to those offering appointments outside those hours.
Downing Street said surgeries should do more to ensure they offered appointments in the evening and at weekends.
'Bad for hospitals'
It said: "Most GPs do a fantastic job, and have their patients' interests firmly at heart.
"However, it is increasingly clear that a large number of surgeries are not providing the access that patients need - and that patients are suffering as a result because they are then forced to go to A&E to seek care.
"It's also bad for hospitals, who then face additional pressure on their services."
The government highlighted October 2015 figures from the National Audit Office (NAO), which showed that 46% of GP surgeries closed at some point during core hours, and 18% closed at or before 15:00 on at least one weekday.
Three-quarters of those that closed early were receiving extra funding in 2015-16 to provide access outside of core hours, the NAO said.
Number 10 also said ministers had been shown evidence that some GP surgeries were failing to tell patients about extending hours for appointments or ensuring they were at convenient times.
It said patients not seen outside working hours were "left with little option" but to go to A&E.
It comes as figures show more than four in 10 hospitals in England declared a major alert in the first week of the new year as they faced unprecedented pressures.
The director of acute care for NHS England, Professor Keith Willett, has estimated that 30% of patients attending A&E would be better cared for elsewhere in the system, the government said.
Downing Street said the prime minister wanted to help reduce pressures on hospitals in a number of ways:
- Ministers may ask GP surgeries to use a new appointments tool to submit appointments data
- GPs would receive extra funding for offering extended hours only if they could demonstrate they were offering appointments which patients wanted and were advertising them properly
- Surgeries receiving extra cash for longer opening times would be asked to expand their online services for patients to free up time for consultations and treatment
'Close to the precipice'
The British Medical Association (BMA) accused ministers of trying to "deflect blame" on to doctors rather than address the NHS funding crisis.
GP committee chairman Dr Chaand Nagpaul said pressure on A&E services was down to seriously ill patients for whom seeing a GP would not prevent a hospital admission.
The government must "take responsibility" and outline an emergency plan to tackle NHS under-resourcing, he said.
Professor Helen Stokes-Lampard, chairwoman of the Royal College of GPs said the "whole of general practice and primary care" was "close to the precipice" after being "under-funded and under-resourced for a decade".
Promises of more staff and resources had yet to reach the front line. She said: "So to put pressure on a system that's already cracking is unhelpful and it's going to demoralise GPs further."
Labour leader Jeremy Corbyn accused the prime minister of being in denial about the state of the NHS.
In a speech in central London, he said Theresa May was blaming the "crisis" on "hard-pressed and under-pressure GPs", not underfunding by the government.
Later, shadow health secretary Jon Ashworth told the BBC that the Conservatives had been promising a seven-day GP service for more than six years.
He said Mrs May's response to the "crisis" in the NHS was "increasingly incompetent and floundering", and urged her to "get a grip of the situation".
Health think tank the Nuffield Trust's chief executive Nigel Edwards said the problem was capacity, not timing.
"If you haven't got more GPs and more practice nurses to do it, you haven't increased the number of appointments, you've just put additional pressure on a service that's already under a very severe level of pressure," he said.
The government said ministers believed GP surgeries had a "vital role" to play in alleviating pressure on A&E.
A 14% increase in funding to general practice will ensure there will be about 5,000 more doctors by 2020, it added.