Denise Fergus, the mother of murdered toddler James Bulger, has allegedly received “vile” and abusive messages from someone posing as her child’s killer under the account @SirJVenables.
Merseyside Police have now launched an investigation following hundreds of complaints on Twitter.
The account has since been suspended after appalled Twitter users called for the social network to act, with many describing the abuse as “sick”.
Liverpool councillor Jake Morrison, who is working with Ms Fergus on a campaign to protect her from receiving further online abuse, said he has also received a threatening message from the same account.
Speaking to The Independent, Cllr Morrison said he believes the same troll has targeted him because of his connection with Ms Fergus. He said he was sent a message he considered to be a “death threat” after uploading a picture of his two-day-old nephew on Twitter.
“I reported it to the police as a death threat,” he said. “I also contacted the managing director of Twitter this morning, and Twitter responded within ten minutes and said they are going to have an urgent meeting with us next week.”
Mr Morrison said Ms Fergus has seen a spike in the number of distressing and abusive messages sent to her surrounding the toddler’s murder since the 21 anniversary of his death last month.
@twitter Please do something about the horrific account sirjvenables absolutely disgusting.— Beverly Macca CBA (@BeverlyMacca1) March 7, 2014
I've seen disgusting profiles on here but @SirJVenables is the worst! Absolutely sick, vile human behind this needs locked up! Report this!!— Marty Strong (@MartyStrong88) March 7, 2014
Please report this disgusting @SirJVenables account. Low life.— Col Talbot (@ColTalbot1) March 6, 2014
"There has been a handful of tweets that are so severe we’ve had to report these to the police – they have been incredibly disturbing,” he added.
Together, Ms Fergus and Mr Morrison called for a meeting with the Prime Minister David Cameron last month to discuss ways of preventing trolls from sending any further abuse, but they have not yet received a response.
In a statement, Merseyside Police said: "Thanks to all who have reported the offensive tweets. An investigation into the account concerned is underway."
James Bulger was abducted, tortured and killed by Venables and Robert Thompson in February 1993. The two boys were jailed for life but released on licence with new identities in 2001.