Children born to fathers with diabetes are around five times more at risk of developing type 1 diabetes as those without it.
Those with mothers with type 1 diabetes have three times the risk, while the offspring of mothers with type 2 diabetes have almost double the chance.
A study, which looked at more than 1.2 million children in Sweden, also found that mothers who were overweight or obese in early pregnancy increased the risk of children developing type 1 diabetes - even if neither parent had the condition.
Researchers said better public health strategies are needed to encourage mothers-to-be to keep to a healthy weight, as type 1 diabetes in children becomes more prevalent all over the world. The latest National Pediatric Diabetes Audit revealed there were 1,000 more children suffering from diabetes reported in England and Wales last year.
In the Swedish study, a high body mass index was associated with a 33 per cent increased risk of type 1 diabetes in offspring of parents without diabetes when compared with maternal BMI in the normal range.
It added that maternal obesity within the three months only increased the risk of diabetes in the children of parents without diabetes, causing no "extra" risk in the offspring of parents with diabetes, suggesting that heredity for type 1 diabetes is the strongest risk factor of the two for development of type 1 diabetes.
"This population-based study from Sweden demonstrates significantly increased risks of type 1 diabetes in offspring of both mothers and fathers with diabetes and regardless of parental migration background," the authors concluded.
"The highest risks were noted in offspring of mothers and fathers with type 1 diabetes.
"Furthermore, maternal overweight and obesity in early pregnancy was associated with increased risk of type 1 diabetes in the offspring of parents without diabetes.
"Therefore prevention of overweight and obesity in women of reproductive age - currently increasing in all countries - may contribute to a decreased incidence of type 1 diabetes."
The research, led by Associate Professor Tahereh Moradi, of the Karolinska Institutet in Stockholm, is published in Diabetologia (the journal of the European Association for the Study of Diabetes).
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