People who eat more saturated fat have a higher risk of an early death, according to a large study that contradicts recent claims that “butter is back”.

The study from the Harvard TH Chan School of Public Health in the United States has been following 126,000 people for three decades to assess the impact of their diet on their health and lifespan. The researchers claim it is the most detailed and powerful examination to date of the effects of eating different types of fats.

Its findings run counter to those of a study published by the National Obesity Forum in May, which said people should eat more fat and fewer carbohydrates and rubbished the nutritional guidelines from Public Health England, which recommend that people should eat less butter and red meat. In the row that followed, several members of the forum, including its clinical director, resigned.

The new paper, published in the prestigious US journal Jama Internal Medicine, says eating trans-fats and saturated fats, including those from red meat and butter, is linked to higher mortality rates compared with the same number of calories from carbohydrates.

More importantly, they say, they found that death rates dropped by between 11% and 19% among people who ate unsaturated fats compared to people who consumed the same number of calories in the form of carbohydrates. Every 5% increase in saturated fat consumption compared to carbohydrates raised the mortality rate by 8%.

Replacing just 5% of their calories from saturated fats – about 15g – with the same amount of polyunsaturated fat such as olive oil was associated with a 27% lower risk of early death.

They had a lower risk of death from not only cardiovascular disease and cancer but also neurodegenerative diseases, such as Alzheimer’s and Parkinson’s, and respiratory disease, compared with people who continued to eat a lot of food containing saturated fats.

Eating carbohydrates instead of saturated fats also reduced mortality rates, but by a relatively small amount.

“There has been widespread confusion in the biomedical community and the general public in the last couple of years about the health effects of specific types of fat in the diet,” said the study’s lead author, Dong Wang, of the departments of nutrition and epidemiology at Harvard Chan school. “This study documents important benefits of unsaturated fats, especially when they replace saturated and trans fats.”

Frank Hu, a professor of nutrition and epidemiology and a senior author of the study, said that in practice “this can be achieved by replacing animal fats with a variety of liquid vegetable oils”.

The study included 126,233 participants from two large long-term studies – a nurses’ health study and a health professionals follow-up study – who answered survey questions every two to four years about their diet, lifestyle and health, for up to 32 years. During the follow-up, 33,304 deaths were documented.

“These findings are consistent with current public health recommendations in the UK and elsewhere, and particularly with the concept of a beneficial Mediterranean-style diet rich in unsaturated fats from plants, fish and olive oil,” said Dr Ian Johnson, emeritus fellow at the Institute of Food Research.

“Recently a number of books and opinion pieces have popularised the idea that conventional dietary advice, recommending consumption of vegetable oils and other products rich in unsaturated fats in preference to saturated fats from animal products, has been shown to be wrong. This study should do much to redress the balance. There is nothing in these results consistent with the notion that ‘butter is back’.”

• This article was amended on 15 July 2016 to clarify some details of the research. An earlier version said researchers had “found that death rates dropped by between 11% and 19% among people who replaced saturated fats such as butter, lard and red meat with unsaturated fats such as olive oil, canola oil and soybean oil”.