For the first time, the association is recommending that people with high blood pressure should eat a diet which is high in minerals and low in fat, in addition to cutting back on salt.
Its Nutrition Committee says research shows a diet high in potassium, calcium and magnesium and low in fat and salt can reduce systolic (top number) blood pressure by an average of 5.5mm of mercury and diastolic (bottom number) blood pressure by 3mm of mercury.
Research shows that reducing diastolic pressure by as little as 2mm can lower a person's risk of stroke by 15% and their risk of heart disease by 6%.
One in four
One in four Americans has high blood pressure, increasing their risk of suffering strokes, heart disease and kidney failure.
Researchers put a group of 459 people with mild hypertension on three different types of diet over an eight-week period.
The first diet was a control; the second was high in fruit and vegetable and the third was low in fat and high in fruit and vegetables. All three diets were low in salt.
The researchers found that a diet rich in fruit and vegetables alone can reduce diastolic pressure by 1.1mm of mercury.
Eat bananas
Fruit and vegetables with a high level of naturally occurring minerals called electrolytes - magnesium, potassium and calcium - include bananas, raisins, potatoes and dates.
Theodore Kotchen of the Nutrition Committee said: "First, this report reaffirms the importance of lowering and avoiding excess salt in the diet.
"Secondly, it indicates that dietary components other than salt are also important in the control of high blood pressure."
The Nutrition Committee is unclear whether the effectiveness of certain kinds of fruit and vegetables in reducing blood pressure is due entirely to their electrolyte content.
Weight loss
And it does not recommend taking high levels of calcium to reduce blood pressure, although it says calcium can reduce the risk of brittle bone disease.
The Committee recommends that people with high blood pressure limit their salt intake to no more than six grams a day.
They should also keep their weight down and avoid drinking more than two alcoholic drinks a day.