However, a higher intake of calcium from foods (820 mg per day) was associated with a 30% lower risk of heart attack. Calcium from foods or supplements was not found to increase or decrease stroke risk.
Previous research has linked higher calcium intake with a lowered risk of high blood pressure, obesity, and type 2 diabetes, all of which are risk factors for heart disease and stroke.
And calcium supplements are commonly recommended to elderly people and women who have gone through the menopause to prevent bone thinning.
The findings are based on almost 23,980 participants of one of the German arms of the European Prospective Investigation into Cancer and Nutrition (EPIC) study in Heidelberg. All were aged between 35 and 64 when they joined the study in 1994-1998.
Normal diet for the preceding 12 months was assessed using food frequency questionnaires and they were quizzed about whether they regularly took vitamin or mineral supplements.
Their health was tracked for an average of 11 years, during which time 354 heart attacks, 260 strokes and 267 associated deaths occurred.
After accounting for factors likely to influence the results, those whose diets included a moderate amount (820 mg daily) of calcium from all sources, including supplements, had a 31% lower risk of having a heart attack than those in the bottom 25% of calcium intake.
But those with an intake of more than 1100 mg daily did not have a significantly lower risk (nor did they have a higher risk). There was no evidence that any level of calcium intake either protected against or increased the risk of stroke. Dietary calcium did not affect the risk of dying from cardiovascular disease.
But when the analysis looked at vitamin/mineral supplements, it found that those who took calcium supplements regularly were 86% more likely to have a heart attack than those who didn't use any supplements.
And this risk increased further among those who used only calcium supplements. They were more than twice as likely to have a heart attack as those who didn't take any supplements.
The authors conclude: "This study suggests that increasing calcium intake from diet might not confer significant cardiovascular benefits, while calcium supplements, which might raise [heart attack] risk, should be taken with caution."
The evidence that dietary calcium is helpful while calcium supplements are not may be explained by the fact that dietary calcium is taken in small amounts, spread throughout the day, so is absorbed slowly in the bloodstream.
Supplements, on the other hand, cause calcium levels in the blood to spike above the normal range, and it is this flooding effect which might ultimately be harmful, they suggest.
The researchers conclude: "We should return to seeing calcium as an important component of a balanced diet, and not as a low cost panacea to the universal problem of postmenopausal bone loss."
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