The Culture, Media and Sport Committee looks set to call chiefs at the micro-blogging site in the autumn to discuss their response to the torrent of abuse.
Committee chair John Whittingdale said MPs were likely to address the subject when they examine the issues surrounding child protection .
"I would have thought it very possible that the committee might want, in the course of our inquiry, to talk to Twitter," he said.
He spoke after Walthamstow MP Stella Creasy and campaigner Caroline Criado Perez held talks with bosses at the site last night to discuss the stream of vile tweets they received at the hands of internet "trolls".
Tory MP Claire Perry was attacked online for her stance on pornography while Labour MP Stella Creasy was targeted after defending a feminist campaigner who had suffered similar abuse.
Ms Creasy, 36, was subjected to threats of rape and death with one threat reading: ?I?m gonna follow you tomorrow and stab and twist so you bleed to death.?
The Walthamstow MP has reported the messages to police and vowed the ?morons? behind them will be brought to justice.
She added: ?This is not about Twitter, this is about hatred of women and hatred of women who speak up.
?Some of those people sending the messages have been absolutely explicit about that.?
Ms Creasy had been speaking out on behalf of Caroline Criado-Perez, 29, who was vilified by so-called ?trolls? on Twitter after leading a successful campaign to have a woman pictured on a new banknote.
Their plight comes after it emerged Ms Perry was also being targeted over her support of curbs on pornography.
Messages sent to the 49-year-old, a special adviser to Prime Minister David Cameron on child abuse on the web, included one that said she would be raped.
She said she had been tempted to shut down her account but ?that would be giving in?.
Ms Criado-Perez said last night that she felt ?under siege? by the trolls, adding: ?It has just been overwhelming, and has consumed my life both physically and emotionally.?
Yesterday an online petition calling for Twitter to introduce a more effective system for reporting abuse had attracted more than 62,000 signatures.
And last night the website said that it plans to include a button for reporting abuse within every tweet.