Over 12,000 people have signed a petition calling for Twitter to have a "zero tolerance policy on abuse" and "to recognise its current reporting system is below required standards".
The petition was set up after feminist campaigner Caroline Criado-Perez was allegedly targeted with violent abuse and rape threats.
Criado-Perez successfully drove the campaign for women other than the Queen to feature on English banknotes.
More top news
A teenager from Bradford who was indoctrinated with 'chilling' extremist views has been jailed for plotting to go to Syria to fight for IS.
Georgina Ferguson was on a carriage behind the one that was bombed. This is her very personal story of 7/7.
HSBC has sacked employees who staged a mock Islamic State-style beheading during a team-building exercise.