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.