Suicide and violent behaviour can cluster within families, possibly because of genetics, epigenetics, and social and environmental influences, the researchers said.
The study examined associations between a full spectrum of parental psychiatric diseases -- including mental disorders, dementia in Alzheimer disease, substance use disorders, schizophrenia, mood disorders, anxiety, personality disorders and suicide attempts -- with attempted suicide and violent offending by children.
The study found that risks for suicide attempts and violent offending in children increased during each of the psychiatric diseases in parents.
While the link between parental psychiatric disease and violent offending by children was found to be stronger for female than male children, the risk of suicide attempts by children remained regardless of gender.
Parents with antisocial personality disorder, cannabis misuse and prior suicide attempt led to the greatest increases in risk for both suicide attempt and violent offending by children.
On the other hand, mood disorders, particularly bipolar disorder in parents caused some of the lowest increases in risk, especially in violent offending by children.
A history of mental illness or suicide attempt in both parents was associated with twice the risk compared with having only one parent affected.
"Psychiatrists and other professionals treating adults with mental disorders and suicidal behaviour should consider also evaluating the mental health and psychosocial needs of their children," said Roger T. Webb from the University of Manchester in Britain.
However, "early interventions could benefit not only the parents but also their children," Webb added in the paper published online by JAMA Psychiatry.
For the study, the team included more than 1.7 million people born in Denmark from 1967 through 1997 and followed up from their 15th birthday.
About 2.6 per cent of the study population first attempted suicide and 3.2 per cent were convicted of a first violent offence during the study period.