The tax could fund healthy school lunches and better health services for diseases caused by high salt intake, especially stroke and heart attacks, he said.
While progress had been made to lower salt content in bread through the Heart Foundation working with the food industry, more work needed to be done to achieve gains in health, he said.
The study found a diet which reached all nutrient recommendations - including salt at under 5.8g a day - was possible at under $9 per day.
Eight sample diets all achieved an ideal salt intake of less than 4g of salt (two thirds of a teaspoon) a day.
Included in the sample diets were familiar meals such as porridge for breakfast and for lunch a cheese sandwich and peanut butter sandwich.
Other sample meals included mince on toast, sausages, potatoes, a tuna pasta dish and a "Pacific-style meal" including tuna, taro and coconut cream.
The healthiest sample diets were the Mediterranean style and an Asian style diet which excluded high-salt sauces such as soy sauce.
The diets were healthier because of higher levels of vegetables and fruit. Professor Wilson said controls on maximum salt levels were relatively easy as people cannot detect minor reductions of salt in food of around 10 per cent annually.
Co-researcher Rachel Foster said it made sense to reduce the burden of strokes and heart attacks on the health system, which should be a priority for government.
The Heart Foundation's food industry setting manager Dave Monro said it supported voluntary measures for sodium reduction in the food industry.
A regulatory approach was not needed, but that didn't rule out the possibility for regulations to be introduced if those voluntary measures were not proving to be successful, Mr Monro said. The study was published in the international journal PLOS ONE.