The research was carried out over 17 years
However, this finding is disputed by a UK expert, who describes the study as "flawed".
The research was carried out by Jeffrey Johnson, of Columbia University and the New York State Psychiatric Institute.
His team tracked more than 700 children through adolescence to adulthood.
The results were adjusted to take account of possible influencing factors, such as family income, childhood neglect or psychiatric disorders during childhood.
Only 5.7% of the adolescents who watched less than an hour of television a day committed aggressive acts in later years, compared with 22.5% of those who watched between one and three hours, and 28.8% of those who watched more than three hours a day.
Professor Johnson, said: "Our findings suggest that, at least during early adolescence, responsible parents should avoid permitting their children watch more than one hour of television a day."
Girl changes
His research, he said, found a strong link between aggression and television for adolescent males - and for females during early adulthood.
However, British expert Guy Cumberbatch, from the Communications Research Group, based in Birmingham, said that the study findings were "highly misleading".
He said that the relatively small number of children who watched less than one hour a day - 88 out of the 700 - represented an extreme which it was unfair to use as a basis of comparison.
He said: "How many families do you know where children watch this amount or less?
"These are highly unusual families - the kind who are more likely to be taking their children to art galleries and museums.
"And there are so few of them compared to the rest of the children studied.
"This is a case of torturing the data to make it fit a theory."