"Kill yourself", "Nobody wants you" and "You are not normal" were some of the comments received by the teenager on the social networking site Ask.fm after she turned to the web for advice when her boyfriend left her.
When she posted photographs of cuts she said she had made on her arms, one commenter wrote: "I hope that one of these days you cut the big vein on your arm and die".
The girl, who called herself "Amnesia", jumped to her death from an abandoned hotel in her hometown of Fontaniva near Padua in northeast Italy on Sunday.
"We can no longer read about young people who take their lives because of threats and psychological pressure," Micaela Campana, a member of parliament from the centre-left Democratic Party, said in a statement.
"That is why I think it is urgent that parliament discuss a law on bullying and cyberbullying soon," said Campana, who has already proposed a draft bill that would increase the punishment for Internet abuse.
Mara Bizzotto, a member of the European Parliament from the Northern League party, also asked the European Commission for stronger EU legislation so that there can be "justice" for the young girl's death.
Prosecutors in Padua meanwhile have opened an investigation into the girl's suicide and are weighing whether charges of incitement to suicide or abuse can be brought against the commenters on the site.
Ask.fm, which was set up in Latvia in 2010 and allows users to pose questions anonymously, has been at the centre of controversy also in Britain
and the United States after suicides of teenagers who received insults.