Previous research has shown older fathers have genetic mutations in their sperm that could cause autistic spectrum disorder (ASD).
But researchers cannot explain why teenage mothers, older mothers and couples with gaps in their ages have an increased chance of their child developing the condition.
Co-author Michael Rosanoff, director of public health research at Autism Speaks (an organisation that sponsors research and raises awareness of autism), said: "Though we've seen research on autism and parental age before, this study is like no other.
"By linking national health registries across five countries, we created the world's largest data set for research into autism's risk factors.
"The size allowed us to look at the relationship between parents' age and autism at a much higher resolution - under a microscope, if you will."
Co-author Dr Sven Sandin, of the Icahn School of Medicine in New York, said: "Although parental age is a risk factor for autism, it is important to remember that, overall, the majority of children born to older or younger parents will develop normally."
The aim of the study was to determine whether advancing ages of fathers or mothers increase autism risk independently, and to what extent each might do so.
Researchers looked at autism rates among 5,766,794 children - including more than 30,000 with autism - in Denmark, Israel, Norway, Sweden and Western Australia.
Dr Sandin said: "After finding that paternal age, maternal age and parental-age gaps all influence autism risk independently, we calculated which aspect was most important.
"It turned out to be parental age, though age gaps also contribute significantly."
The researchers found autism rates were 66 per cent higher among children born to fathers more than 50 years old than among those born to fathers in their 20s.
And they were 28 per cent higher when fathers were in their 40s, compared to in their 20s.
Mothers over 40 had a 15 per cent increased risk of having a child with the syndrome, compared to those who were in their 20s.
Meanwhile children born to teenage mothers were 18 per cent more likely to have autism than children born to women in their 20s.
The research also showed autism rates rose higher still when both parents were older.
The rates also rose with widening gaps between two parents' ages.
Incidences of autism were highest when fathers were between 35 and 44 and their partners were 10 or more years younger.
Conversely, rates were high when mothers were in their 30s and their partners were 10 or more years younger.
Previous research has shown that genetic mutations in sperm increase with a man's age and that these mutations can contribute to the development of autism spectrum disorders (ASD).
By contrast, the risk factors associated with a mother's age remain unexplained, as do those associated with a wide gap between a mother and father's age.
Dr Sandin added: "These results suggest that multiple mechanisms are contributing to the association between parental age and ASD risk."
The study was published in the journal Molecular Psychiatry.
Dr Judith Brown, of the National Autistic Society (NAS), said: "This is a substantial piece of research with a large sample size which adds to our understanding of the complex causes of autism.
"However, the study is not definitive and, as the authors recognise, there are a number of confounding variables which are not explained and more research needs to be done before any definitive conclusions can be drawn.
"We therefore urge parents and those thinking of starting a family not to worry unduly about these research findings or allow them to affect the decisions they make.
"We still don't understand the full causes of autism, a lifelong condition which affects more than 1 in 100 people in the UK.
"But evidence suggests that autism does not result from a single cause and is rather a complex story of genes interacting with other genes, combined with environmental factors."
Why are older fathers more likely to have children with autism?
In order to produce new sperm, so-called sperm 'precursor' cells have to divide.
They do this every 16 days, which means by the time a man reaches 70, these cells will have divided around 1,500 times.
With each division comes a risk of DNA mutation and genetic defects.
A study from Iceland in 2012 found that the average child born to a 20-year-old father has 25 DNA mutations in their genes and that the number increases annually, reaching 65 mutations for offspring of 40-year-old men, increasing the risk of problems.
It is thought that these mutations can contribute to the development of autism spectrum disorders (ASD).
- Daily Mail