School boards should have a legal right to veto sex education material in classrooms, according to the Tories.
The Tories are concerned about STDs and unwanted pregnancies
The party also wants parents to have the legal right to withdraw their children from sex education classes.
The Scottish Tories' health spokeswoman Nanette Milne has called on the Scottish Executive to affirm the importance of family values.
She said schools were shouldering too much of the burden of educating Scotland's youngsters in sexual health.
Her calls came as the Scottish Parliament debated the executive's new sexual health strategy, unveiled in January this year.
Dr Milne told the chamber the sexual liberation of women since the introduction of the Pill had resulted in some negative consequences.
She said: "The easy availability of alcohol, the increase in drug taking, decrease in religious influence and the open acceptance of extra-marital sex put pressure on girls and women, often resulting in promiscuity and unprotected sex.
"The downside is sexual transmitted infection, unwanted pregnancies and unstable relationships."
She said growing numbers of people were contracting sexually-transmitted infections, like chlamydia, and that a third of 15-year-olds in a recent survey claimed to have had a full sexual experience.
Calling for the issue to be tackled quickly, Dr Milne said there had to be a "very clear focus on family values".
She said: "The executive should very publicly affirm the primary responsibility of parents, ensuring that children are brought up with respect for themselves and others and show how to take responsibility for their own welfare and actions."
The North East Scotland MSP said the passing of responsibility for sexual well-being to schools was "symptomatic of many of the social problems facing communities in Scotland today, whereby parents refuse to take the necessary responsibility for their children's actions".
Turning her attention to the schools themselves, the spokeswoman said parents must play a role in choosing literature used in their children's classrooms.
Stable relationships should be emphasised
Dr Milne said: "They must be given the opportunity to discuss these very sensitive issues with their children in the manner that they see as appropriate.
"We therefore consider the school board should have a legal right to veto any sex education material and parents should have a legal right to withdraw their children from sex education."
But Labour backbencher Scott Barrie warned that the Tories' "over-emphasis" on the role of parents "ignores the fact that some parents are either unwilling or unable to ensure their children are properly informed".
Scotland's new strategy is the outcome of five years of highly-charged debate over the balance between providing advice and access to contraception and the right of faith groups to educate youngsters in line with their beliefs.
The £15m drive intends to bring changes to sex education in schools, where youngsters will be taught the virtues of abstention.
Health Minister Andy Kerr told the chamber parents had a key role in protecting the health of their children.
"Ultimately, however, it is important that we all as individuals take responsibility for our own sexual health," he added.
Good progress had been made, but issues of inaccessible and inappropriate services would not be addressed overnight.
"This is the start of a long journey but I am confident that we can move forward with speed and purpose," he said.
SNP health spokeswoman Shona Robison commended the executive's strategy but criticised the level of funding involved.
She said the £15m figure was "somewhat less of a figure" than the £300m budget announced for a similar programme in England and Wales.