The Joint Public Issues Team's comments follow an investigation by The Sunday Times, which revealed gambling firms are using children's cartoon characters to promote online betting.
The Gambling Commission's Young People and Gambling Report indicated that 450,000 children are gambling in England and Wales every week.
The Advertising Standards Agency has opened an investigation to see if online bookies have targeted youngsters with characters such as Peter Pan and Jack and The Beanstalk, for games - some of which can be played for free, without any age verification required.
Rachel Lampard, team leader of the Joint Public Issues Team, told Premier why this is problematic.
Speaking during News Hour, she said: "Children find it attractive, they have fun, they might even win some money - they can't collect it...but they think they've won.
"It gives this message that gambling is an ok activity for children and that's a really big problem."
Betting firms are not permitted to target children under 18-years-old.
Lampard urged parents to have conversations with their children about their online activities as gambling can have a long-lasting negative effect on them.
She explained: "It leads to disruptive relationships, it leads to truancy, it can lead to stealing, it can lead to deterioration in mental health.
"All of those can have a massive impact not just on children as they grow up - but if that happens at a really important time in their formation as well, it can really affect them as an adult as well."
