Months of investigation by ZDNet UK News has shown that children are being groomed by pedophiles who are now using voice chat as well as text to lure children into meetings.
According to reports, Liberal Democrat Paul Burstow told Blair that a 12-year-old in his constituency had been "groomed" by a pedophile while in an Internet chatroom.
The grooming process is designed to convince vulnerable children that sexual relations with adults are acceptable.
Burstow is reported as asking: "Will you take steps to review the law to ensure that such online grooming is a criminal offence and also use pressure, and bring it to bear on Internet service providers, so that they offer parents chat-free services so that all of our children can be protected?"
Blair is said to be considering the implications of new legislation "carefully."