Theresa May has expressed frustration at the failure of more GP surgeries to offer extended opening hours amid intensifying pressure on NHS hospital services.
The Prime Minister made clear her determination to press ahead with plans for surgeries in England to open 8am to 8pm seven days a week unless they can prove the demand is not there from patients.
There is increasing exasperation among ministers that lack of GP appointments is driving patients to seek treatment in hard-pressed hospital accident and emergency departments.
The director of acute care for NHS England Professor Keith Willett has recently estimated that 30% of the patients attending A&E would be better cared for elsewhere in the system.
Meanwhile the latest official figures showed more than four in 10 hospitals in England declared a major alert in the first week of the year as services came under increasing pressure.
A Downing Street source 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 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."
Ministers say they are providing an additional £528 million a year for practices by 2020/21 to ensure that the target for providing seven-day opening is met by that date.
However they are concerned by a recent finding by the National Audit Office that 46% of GP surgeries were still closing at some point during "core" weekday working hours, despite three-quarters of them having received extra funding to provide extended cover.
They also suggest some surgeries are failing to advertise the availability of extended hours appointments and GPs will be warned future additional cash will be contingent on them demonstrating they are offering appointments when patients want them.
Ministers are now considering asking surgeries to use a new online appointments tool to submit data on the numbers and types of appointments they offer so they can better understand patient demand.
They point to innovative schemes such as the integrated South Kent Coast pilot - which brings together 18 practices offering extended access to services for 110,000 patients - as an example of what can be achieved.
The Government says that so far 17 million patients have benefited from extended access to appointments and that it is committed to increasing the numbers of doctors in general practice by around 5,000 by 2020.