In contrast, raising the animal protein share of calories by 10 per cent led to a 2 per cent higher risk of all-cause death and an 8 per cent greater chance of dying from a heart problem.
"Overall, our findings support the importance of the sources of dietary protein for long-term health outcomes," said Dr Mingyang Song, the lead scientist, from Massachusetts General Hospital.
"While previous studies have primarily focused on the overall amount of protein intake - which is important - from a broad dietary perspective, the particular foods that people consume to get protein are equally important.
"Our findings suggest that people should consider eating more plant proteins than animal proteins, and when they do choose among sources of animal protein, fish and chicken are probably better choices."
Animal protein foods include all types of meat, fish, eggs and dairy products such as milk and cheese. Plant sources of protein include cereals, beans, nuts, legumes, soya and bread.
The greater risk of dying linked to eating animal protein was more pronounced among people who were obese, had a history of smoking, drank heavily, and who did little exercise.
Among the healthiest participants, the association disappeared - possibly because health-conscious people tended to eat more fish and poultry rather than red and processed meat, said the researchers.
Prof Tim Key, director of Oxford University's Cancer Epidemiology Unit, said the findings showed that cutting out processed meat was crucial to good health.
"Few previous studies have specifically addressed the relationships of mortality with animal versus plant protein, but previous long-term studies on major animal and plant foods are broadly consistent with these findings, and there are several mechanisms which could explain the findings," he said.
"Overall, the study adds to the view that healthy diets should emphasise plant foods, including plant sources of protein, and that intakes of animal source foods - especially processed meat - should be low."
The researchers analysed more than 3.5 million person-years of data in the study.
Dr Ian Johnson, from the Institute of Food Research in Norwich, said: "This interesting and robust work seems to support the growing consensus that diets based largely on plant foods are better for long-term health than diets containing large quantities of meat and dairy products, but it tells us little about mechanism.
"It is far from clear whether plant proteins are protective or animal proteins are detrimental to health, or whether these protein levels are simply markers for something else."
The findings are reported in the journal Jama Internal Medicine.