Prime Minister Kevin Rudd said he would consider introducing an internet ombudsman after Facebook tributes to two dead children were defaced with pornography.

Rudd said he would look into an idea put forward by Independent Senator Nick Xenophon to appoint an official who would be responsible for taking complaints and action against such material.

"We actually need to do everything we can to combat cyber crime," Rudd said.

"The role of cyber crime and internet bullying on children is, frankly, frightening and we need to be deploying all practical measures."

Memorial pages on the social networking site for eight-year-old Trinity Bates and Elliott Fletcher, 12, who were allegedly murdered in separate incidents this month, have been vandalised with offensive material.