GPs from the Deep End Group, which works in the most deprived areas of Glasgow, said there are too few doctors and appointment times are not sufficient to meet patients' needs.
The GPs told the Scottish Parliament health committee that there is still a lack of resources in deprived areas and some social groups were able to make better use of the health service than others.
Professor Graham Watt, representing the General Practitioners at the Deep End, said: "Most causes of poor health and health inequalities operate outside the health service but the NHS can exacerbate them if care is delivered inequitable, on the basis of need.
"The solution is not simply an increase in the number of general practitioners, although additional clinical capacity is needed to relieve the pressure on existing staff and to enable new developments in care.
"We propose an extra GP session per week per 1000 patients with addresses in the 155 most deprived datazones."
A team from Greater Glasgow and Clyde Health Board which has been working on access to services in deprived areas found a number of barriers to accessing health services.
A written report to the committee stated the cost of travelling to appointments and ability to attend appointments around working time was an issue.
It found some services were too complex, with people with multiple health issues more common in deprived areas, meaning more appointments.
It also found some services failed to recognise underlying issues like domestic violence, financial difficulties or welfare reform and their impact on health.