Other patterns of symptoms, such as chronic depression, appear not to be linked, a study found.
Dutch researchers looked at different ways depression in older adults progressed over time and how this related to any risk.
They concluded worsening depression may signal the condition is taking hold.
The research, published in The Lancet Psychiatry, followed more than 3,000 adults aged 55 and over living in the Netherlands.
Dr M Arfan Ikram of the Erasmus University Medical Center in Rotterdam said depressive symptoms that gradually increase over time appear to be a better predictor of dementia later in life than other paths of depression.
“There are a number of potential explanations, including that depression and dementia may both be symptoms of a common underlying cause, or that increasing depressive symptoms are on the starting end of a dementia continuum in older adults,” he said.
Only the group whose symptoms of depression increased over time were found to be at increased risk of dementia – about one in five of people (55 out of 255) in this group developed dementia.
Others who had symptoms that waxed and waned or stayed the same were not at increased risk.
For example, in those who experienced low but stable levels of depression, around 10% went on to develop dementia.
The exact nature of depression on dementia risk remains unknown.
They often occur together, but the Dutch study is among the first to look at different patterns of depression symptoms.
Dr Simone Reppermund from the Centre for Healthy Brain Ageing at the University of New South Wales, Sydney, said more studies were needed to understand the link.
“A focus on lifestyle factors such as physical activity and social networks, and biological risk factors such as vascular disease, neuroinflammation, high concentrations of stress hormones, and neuropathological changes, might bring new treatment and prevention strategies a step closer,” she wrote in a linked editorial in the journal.
Depression varies greatly from one person to another. Some experience depressive symptoms only briefly, others have remitting and relapsing depression and some people are depressed all the time.
Dr Simon Ridley, director of research at Alzheimer’s Research UK, said anyone concerned about either condition should seek help.
“The findings suggest that low levels of depression or fluctuating symptoms may not affect dementia risk but that a worsening of symptoms in the over-55s may be an early indicator of diseases like Alzheimer’s,” he said.
“It’s important to remember that only a relatively small number of people experiencing symptoms of depression went on to develop dementia during this 11-year study, but anyone concerned about either condition should talk to their GP.”