Reform Scotland has also said all surgeries should have a website and provide clearer information for patients.
It made a series of recommendations it believes would help patients in picking a practice that provides services suited to them.
In a report, the independent organisation said research showed where a patient lives will often determine whether they can attend an evening or weekend surgery, or order repeat prescriptions online. By expanding a practice's catchment area, Reform Scotland believes patients will be provided with a meaningful choice, which will drive up standards.
Director Geoff Mawdsley said: "Reform Scotland believes it is simply unacceptable that there is such a wide variation in the way people can access GP services, whilst there is little or no choice over where they can register."
The paper, Patients First: Improving Access to GP Practices, also recommends allowing new surgeries to open up to further increase choice and improve services. It said it believes the ban on private-sector companies opening GP practices should end.
However, doctors' leaders said they disagreed strongly with the recommendations.
Dr Alan McDevitt, chairman of the British Medical Association's Scottish general practitioners committee, said that while the report had picked up on the important issue of access, he "could not disagree more" with their proposed solutions.
"What some call postcode lottery others would call local flexibility. A proportion of services provided by practices are agreed locally between the health board and individual practices according to local priorities," he said. "In the case of extended hours, for example, what is the point of a GP spending time running a late surgery if there is no demand for it locally? We will always have to work to improve access as there is no 'perfect' solution.
"Patients across Scotland can choose from a number of local GPs, with some obvious exceptions, such as in rural areas. The idea that we should expand our practice boundaries demonstrates a clear lack of understanding of the reality of the work and structure of general practice."
Mr Mawdsley said expanding the catchment area would not put extra pressure on practices as they would still be able to close their lists to new patients if they reached capacity.
He said: "In practice, many people would still prefer to join the practice closest to them. However, by enabling patients to move and go elsewhere if they are unhappy with the way they can access services where they are, there is greater pressure on all GP practices to improve.
"Our recommendations are sensible, practical and, most importantly, easily introduced."
In response to Reform Scotland's call to allow private companies to run GP practices, Dr McDevitt said: "This report seems to think that the independent contractor status of GPs is the same as services that could be provided by large multinational companies like Virgin Healthcare or Atos. They couldn't be more wrong.
"The independent contractor status does mean that GPs are not directly employed by the NHS, but it also means that they are small and agile and can adapt to immediate demands – such as the provision of care during the swine-flu pandemic.
"Ultimately, the political decision has been taken to legislate to prevent commercial companies providing GP services in Scotland. That is a decision that has been welcomed and supported by the BMA."