The international drug control system is "floundering" for the first time in the face of the rapid rise of potentially harmful legal highs or new psychoactive drugs, the United Nations has warned.

The UN's annual world drug report says the number of new legal highs available on the world market – more than 300 – has now outstripped the total number of illicit drugs under international control.

The 2013 report published on Wednesday says the newly developed legal high industry has gone global in the past year, with 70 out of the 80 countries surveyed reporting the emergence of new psychoactive substances with significant market share.

The UN's office on drugs and crime (UNODC) says the speed and creativity in the emergence of these new designer drugs has left the international drug control system floundering for the first time since its establishment in 1961.

It warns that far from being "low-risk fun", the new generation of drugs sold online are untested for safety and are potentially far more dangerous than traditional drugs such as cocaine and cannabis, the markets for which have remained stable.

The report says the use of legal highs has taken off most strongly in the US, where 11% of 17- and 18-year-olds say they have used them. They are now the second most popular class of recreational drug among American students after cannabis.

This is twice the level of use reported among European teenagers, of whom 5% of all 15-to-24-year-olds say they have already experimented with legal highs. Britain accounts for nearly a quarter of the entire legal high market in Europe,followed by Poland (17%), France (14%) and Germany (12%).

But the new psychoactive phenonema is also making inroads into Latin America, Asia and parts of Africa. Brazil has reported the emergence of mephedrone and plant-based substances such as Salvia divinorum. But their use is also now reported in China, Japan and Indonesia. In the African continent, Angola, Egypt, Ghana, South Africa and Zimbabwe all reported to the UN the emergence of these drugs in the past year.

"Marketed as legal highs and designer drugs, new psychoactive substances are proliferating at an unprecedented rate and posing unforeseen public health challenges," says the report. UNODC's executive director, Yury Fedotov, said a UN early warning system and concerted action to prevent the manufacture, trafficking and abuse of these substances was needed.

"This is an alarming drug problem – but the drugs are legal. Sold openly, including via the internet, psychoactive substances which have not been tested for safety can be far more dangerous than traditional drugs.

"Street names such as 'spice', 'meow-meow' and 'bath salts' mislead young people into believing they are indulging in low-risk fun. Given the infinite scope to alter their chemical structure, new formulations are outpacing efforts to impose international controls," says the UN report.

"While law enforcement lags behind, criminals have been quick to tap into this lucrative market. The adverse effects and addictive potential of most of these uncontrolled substances are at best poorly understood."

The most popular legal highs imitate the effects of more traditional drugs such as cannabis and ecstasy. They are synthesised by chemists operating out of south-east Asia and sold globally through a mushrooming network of internet shops. As soon as authorities are able to ban one set of chemical compounds in one jurisdiction, the chemists simply adjust the chemical structure to produce a different derivative that is not caught by the legal ban.

The G8 group of countries published a new international agreement on Tuesday on tackling legal highs. The agreement is designed to improve information sharing on the new substances including their impact on public health and on supply routes.