Police are investigating a series of sexually explicit and violent tweets sent to Labour MP Stella Creasy.
The politician retweeted some of the messages to her 30,000 followers and warned the senders would face justice.
The abuse from internet "trolls" came after she backed a feminist campaigner who had received online rape threats.
John Whittingdale MP, chairman of the Commons Culture, Media and Sport Select Committee, said it wanted to question Twitter about its response to abuse.
The committee is holding an inquiry into harmful online content and child protection, but Mr Whittingdale said it could also look at the issue of "trolling" - the use of social networking accounts by individuals or groups to write abusive messages to others.
"It isn't that the law needs to be changed; the question is how you identify people and how you prevent them [from abusing others]," he said.
"That is the big question and it is one we would wish to explore with internet companies to determine whether they are doing as much as they can or whether they should do more."
Caroline Criado-Perez was harassed after her successful campaign to have author Jane Austen on the new £10 note.
She reported the matter to police after receiving "about 50 abusive tweets an hour for about 12 hours" and said she had "stumbled into a nest of men who co-ordinate attacks on women".
A 21-year-old man arrested on suspicion of harassment offences has been bailed to a date in mid-September.
Ms Criado-Perez described how the online abuse had left her feeling "under siege" and terrified in her own home.
She told BBC Two's Newsnight: "It has consumed my life both physically and emotionally. I've not really had much sleep.
"The threats have been so explicit and so graphic that they've sort of stuck with me in my head and have really put me in fear."
Ms Creasy, the MP for Walthamstow, reported the barrage of abuse directed at her to the Metropolitan Police on Monday night.
She had warned the senders that she would report them. "You send me a rape threat you morons I will report you to the police & ensure action taken," she tweeted.
Scotland Yard said "officers in Waltham Forest received an allegation of malicious communications from an MP. The allegation relates to comments made on Twitter and is currently under consideration".
Rules of conduct
On Monday, Andy Trotter, chairman of the Association of Chief Police Officers communications advisory group, said had to "take responsibility as do the other platforms to deal with this at source".
Twitter said manually reviewing every tweet was not possible due to the micro-blogging site's global reach but there were systems in place to report those users who broke its rules.
Del Harvey, senior director for trust and safety, said: "These rules explicitly bar direct, specific threats of violence against others and use of our service for unlawful purposes, for which users may be suspended when reported.
"To the extent that our system is based around the filing of reports with our trust and safety team, we strive to make it easier and more practical to file them.
"Three weeks ago, we rolled out the ability to file reports from an individual tweet on our iPhone app and the mobile version of our site, and we plan to bring this functionality to Android and desktop web users."
More than 72,000 people have so far signed an online petition demanding that Twitter introduce a "report abuse" button and review its terms and conditions on abusive behaviour.
The recent cases have led other people to come out and talk about the abuse they receive via Twitter.
Claire Perry, the Conservative MP for Devizes who has been advising the prime minister on measures to tackle the spread of extreme pornography and child abuse on the internet, tweeted: "I am tempted to shut down my Twitter account given the trolling going on incl. to me - but that would be giving in #TakeBackTwitter."