Mr Neil was responding to yesterday's exclusive story in the Evening Times – in which a group of Glasgow GPs described how a 20-year failure to address health inequalities in the city has left people in poorer areas to suffer while the rest of the city enjoys improving health standards.
The doctors said that while health in the city is improving generally, people in poorer areas are not getting healthier as fast as those living in more affluent surroundings.
They called on more doctors and extra funding to be targeted at poorer areas to tackle the problem.
Today, Mr Neil vowed to do what he could to narrow the health gap, but warned that change won't come overnight.
Mr Neil said: "Improving health equalities – closing the health gap between the richest and poorest people – is one of our greatest challenges.
"Scotland and Glasgow's health is improving, with people now living longer, healthier lives.
"Yet there are still anumber of areas, like rates of cancer or healthy life expectancy, where there is no clear evidence that the gap is closing.
"The causes of health inequalities are extremely complex and concentrating solely on health solutions will simply not end the problem.
"So while putting more doctors in deprived areas may help, it does not solve the causes of ill health."
The problem won't be solved by fixing the symptoms, Mr Neil said, and instead he insisted he was looking into developing a plan to tackle the underlying causes.
He said: "I am clear that we need to shift the emphasis of our approach from dealing with the consequences of health inequalities to tackling the underlying causes such as poverty, support for families and poor physical and social environments.
"The Ministerial Taskforce on Health Inequalities is looking again at all available evidence to see if we can find new or better ways to improve health equality.
"The impact of our environment on health is huge.
"We also need to make sure we give people safe access to leisure facilities, regular exercise increases mental and physical wellbeing and life expectancy.
"Studies have shown time and again that early life conditions influence adult health.
"Adverse childhoods translate into poorer education, increased offending, higher risk of suicide, depression, alcoholism and obesity.
"So our Early Years Framework approach places a strong emphasis on giving children, particularly those who are most disadvantaged, the best possible start in life.
"More than 750 early years experts – a coalition of social services, health, education, police and third sector professionals – gathered in Glasgow last week to start to work towards new and ambitious aims to improve children's start in life.
"That is precisely the kind of collaboration we need across the public sector, working with people offer new opportunities."
Mr Neil said that UK Government welfare cuts are already having a huge impact on families and vulnerable groups – cuts he described as "extremely worrying".
He added: "In the current political and economic circumstances, we are doing what we can, alongside all of our partners, to tackle poverty and inequality and help people get into work.
"Our long-standing problems won't be solved overnight, but we can make a difference and the Scottish Government will do what it can to narrow the health gap."