Leitrim schoolgirl Ciara Pugsley also took her own life after being harassed on the site, which is often accessed via Facebook.
Lancashire girl Hannah Smith took her own life last Friday.
Her father David urged parents to stop their children using the Latvian-based Ask.fm. Mr Smith called for its creators to be prosecuted for manslaughter.
Less than a fortnight before her body was found early last Friday, Hannah begged her tormentors – who can hide behind a cloak of anonymity on the site – to stop the abuse.
In another post, she told one bully who had branded her an “ugly f*****” how she had already attempted suicide and added: “Getting things like this from people that like to hide behind there (sic) computer screen doesn’t make me feel any better.”
Her dad said at the weekend: “I have just seen the abuse my daughter got from people on ask fm and the fact that these people can be anonymous is wrong. The person that created this website should be done for manslaughter.”
In her final days, Hannah had been branded a “cow” and “fat sl**”.
On July 20, a troll wrote, “* ugly f*** go die evry1 wuld be happy”, prompting Hannah to reply: “yes, i may be ugly, but you obviously have an ugly personality to tell people to ‘go die’!”
Other hurtful posts urged her to “do us all a favour * kill ur self” and “go comit suicide”. Hannah replied: “wouldn’t you fell bad if I did ey?#8221; Just the day before she apparently killed herself, Hannah posted a picture message on Facebook which read: “You think you want to die, but in reality you just want to be saved.”