Over 3,200 crimes including knife carrying, assault and sexual exposure were alleged to have been committed by children under 10 in the past three years, according to data collected by the Conservatives.
Figures from Scotland's eight police forces apparently show that 1,095 crimes among under-10s were reported to police in 2011-12, up from 1,059 in 2010-11 and 1,048 in 2009-10. The alleged crimes also include instances of breach of the peace, vandalism and racially aggravated conduct.
The data says that in Strathclyde, two eight-year-olds were found carrying knives and two nine-year-olds were reported for a sexual assault on a girl. Strathclyde was said to have the highest rate of reporting for child offending in Scotland last year, with 212 reported incidents.
Scottish Conservatives leader Ruth Davidson said: "These results are shocking. Here we have primary school children breaking the law: carrying weapons, harming people and destroying property.
"If the Scottish Government does not get a handle on this, it will result in the nurturing of a generation of future criminals who will go on to regular and more severe offending. We need to ensure this number drops sharply, and stop these children in their tracks before they ruin both their own lives and the lives of others.
"We also have to question what thousands of parents are doing when their young children are out, presumably unsupervised, tearing up the streets of Scotland."
Under Scots law, children under the age of eight are not held criminally responsible for their actions but can be referred to the Children's Hearing System on welfare grounds. Children over eight but under 12 can be dealt with at children's hearings. Only those aged 12 and over can be prosecuted in court, if the offence is deemed sufficiently serious.
A Scottish Government spokesman said: "These figures reflect reported and alleged rather than actual offences. Latest statistics show that Scotland is becoming safer, with recorded crime at its lowest level in 37 years, a record number of police officers out on the streets protecting our communities and offence-referrals to the Children's Reporter have fallen for the fifth consecutive year, by 66% since 2006-07.
"However, there is still more to do, and behaviour by children which comes to the attention of the police is always particularly worrying. These kids should be out enjoying positive activities rather than going down the wrong path in life.
"That is exactly why we are investing so heavily in providing so many sporting and outdoor diversionary activities for young people right across the country to get involved in, through the Cashback for Communities Programme where more than £46 million has so far been invested."