Young children are routinely witnessing upsetting or explicit material online and many are being targeted by strangers, according to research commissioned for Safer Internet Day.
A Kaspersky Lab study revealed that almost a quarter of parents takes no action to govern their children's online activity, whether on the home computer or mobile devices.
"Regardless of how their children are accessing the internet, parents must remain vigilant, supervise their internet use and consider parental control technologies," said David Emm, senior security researcher at Kaspersky Lab.
"When children use mobile devices to access the web, they are using the same internet, with the same risks – yet parents are often not as aware of the dangers."
As many as two million children under the age of sixteen claim to have been approached by strangers online, often without their parent's knowledge.
Paul Martini, CEO at iboss Network Security, believes that more needs to be done to rectify this situation.
"Parental teaching of key Internet safety issues needs to be just as common as warning children not to get into a car with a stranger," Martini said. "Safety is built on education, boundaries and a watchful eye at home and at school.
"There needs to be an advanced security platform with the new web that goes beyond basic web filtering," he added. "And, schools need to take granular control of what students can access whilst within the school grounds. The Internet cannot be left wide open."
A separate study commissioned by the BBC found that almost 20 per cent of children had witnessed upsetting content on their smartphone or tablet device.
Despite this, many parents continue to allow their children to surf the internet without parental controls or supervision.
"Unfortunately, none of us - of whatever age - is immune from encountering problems online," Tony Neate, chief executive of Get Safe Online, told the BBC.
"Without using controls such as built-in security, safety and privacy features and search engine filters, children will almost certainly run into something that really isn't appropriate for their age, or any age."
Both studies were released in conjunction with Safer Internet Day, an annual campaign intended to promote safe use of the Internet for children and young adults.
Will Gardner, director of the UK Safer Internet Centre, believes that the range of supporters – from both public and private sectors – reflects "how widespread and important this issue is".