Health Secretary Alan Johnson has said he does not want to change the 2004 contract, which allowed GPs to opt out of providing out-of-hours care.
And while he said he will not adopt a "confrontational approach" with family doctors, he reiterated his call that surgeries must be more accessible for patients.
He said: "GP surgeries should be open at times and in locations that suit the patient, not the practice."
One potential move may be for pharmacies, sports halls and high street walk-in centres to take on some of the roles of providing care.
But Mr Johnson said he intends to work with GPs and the British Medical Association (BMA) to develop a "much more convenient service".
He added more people should be able to choose which GP they go to – but conceded there are problems in some areas with a shortage of practices.
"What I want is to focus absolutely remorselessly on patient care – how we can improve patient care. And part of that is empowering patients to say I'm not getting good care with this GP, I'll go to another GP," he said.
Asked if that means GPs will have to compete against each other, he said: "In a sense, that's true, but I don't think it would work on the basis of, you know, Tesco versus Asda."
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"Nothing wrong with a little, bet we can't recipricate though!" – Name and address supplied
"Would the 13% of our patients who do not like our access please choose another GP, as Mr Johnson has suggested - then we will hit 100% and all will be happy!" - Name and address supplied