The research suggested low level distress raised the risk by 16%, once lifestyle factors such as drinking and smoking were taken into account.
More serious problems increased it by 67%, the University College London and Edinburgh University team said.
The risk among those with severe mental health
problems is already well documented.
But researchers said the finding among those with milder cases - thought to be one in every four people - was concerning, as many would be undiagnosed.
The Wellcome Trust-funded study, published in the British Medical Journal, looked at data over 10 years and matched it to information on death certificates.
This is the largest study so far to show an association between psychological distress and death, according to scientists.
Lead author Dr Tom Russ said: "The fact that an increased risk of mortality was evident, even at low levels of psychological distress, should prompt research into whether treatment of these very common, minor symptoms can modify this increased risk of death."
John Williams, head of neuroscience and mental health at the Wellcome Trust, said: "This study highlights the need to ensure they have access to appropriate health care and advice so that they can take steps to improve the outcome of their illness."
Paul Jenkins, chief executive of the charity Rethink, said: "Sadly, these findings do not come as a surprise.
"While this study looks at depression and anxiety, people with severe mental illnesses such as bipolar disorder and schizophrenia die, on average, 20 years earlier than the rest of us. It's an absolute scandal.
"There is a huge lack of awareness amongst health professionals about the increased risk of physical illness for this group, which means people are dying needlessly every day."
Marjorie Wallace, the chief executive of the mental health charity SANE, said: "Even what may be considered mild depression can cut short a person's life, not only through the use of alcohol, cigarettes and other substances, but by directly affecting the recovery from physical illnesses such as heart disease.
"The debilitating effects on a person's life can lead them to neglect themselves and their management of long-term conditions such as diabetes or cancer."