The House of Commons culture committee is planning to question top Twitter executives following abusive tweets directed against Labour MP Stella Creasy.
Creasy complained to police after receiving rape and death threats on the social networking site, after another complaint from Tory MP Claire Perry who alleged that she received similar threats.
The move from the committee follows recent abusive posts to journalist Caroline Criado-Perez, who was threatened with rape tweets for her campaign to keep women on British banknotes.
John Whittingdale, the Conservative chair of the committee, said he expected the abuse directed at Creasy and Criado-Perez to feature in an inquiry starting in the autumn.
Whittingdale told the Guardian: "The law is perfectly adequate. If someone posts a message on Twitter saying he's going to rape you, that is a criminal offence already. The challenge is how you identify people and prevent it."
More than 40,000 people have signed a petition for Twitter to improve response to abuse reports and to take a zero tolerance policy towards abuse.
Twitter executives may be asked to give evidence to Parliament over the tweets.
A 21-year-old man from Manchester has been arrested on suspicion of harassment offences in connection with the abuse of Criado-Perez.