Labour MP Stella Creasy says her staff at her office have received abusive phone calls over the Syria airstrikes vote as she attempts to listen to the ongoing debate in the Commons.
Ms Creasy is undecided whether to back military action in a vote later today.
Nick Clegg welcomed police action over Twitter abuse after a man was arrested on suspicion of harassment after threats were aimed at a feminist campaigner on the social networking site.
It comes after Caroline Criado Perez faced a deluge of threats on Twitter over the course of more than a day after she successfully campaigned for a woman's picture to be put on a new bank note.
The Deputy Prime Minister said: "What is unacceptable offline is unacceptable online."
He added that he had "probably" received lots of abuse on Twitter.
Twitter bosses are to be called before MPs' to explain their response to abuse posted on the social networking website.
A 25-year-old man was arrested today on suspicion of harassment by officers investigating Twitter abuse aimed at Feminist campaigner Caroline Criado-Perez and Labour MP Stella Creasy.
The head of trust and safety at Twitter, Del Harvey, told ITV News that policies were in place to protect users against harassment but agreed it could do more to tackle online abuse.
ITV News UK Editor Lucy Manning reports:
Del Harvey, head of trust and safety at Twitter, has said that the company's policy is: "We don't want people to use our platform to do things that are illegal that's not something that we support."
"I think a lot of times people think that we stand on the whole 'Twitter is a platform for free speech - so anything goes' and that's just not the case," she said.
"We do have policies against a lot of harassment ... and a threat of rape or violence is not something that's protected by that sort of concept of anything goes."
Feminist campaigner Caroline Criado-Perez says Twitter needs to "get a grip" on security as it emerged bosses were likely to face a grilling from MPs.
The campaigner, who was besieged with sexually explicit threats on Twitter after she campaigned for the faces of women to be included on banknotes, said the social network was ill-equipped to handle episodes of sustained abuse and needed to work more closely with police to deal with internet trolls.
Ms Criado Perez, 29, met Twitter directors on Monday along with MP Stella Creasy who received a similar torrent of abusive messages after she offered support to the freelance journalist.
A 25-year-old has been arrested on suspicion of harassment by officers investigating Twitter abuse aimed at Caroline Criado Perez, 29, and Walthamstow MP Stella Creasy, Scotland Yard said.
A police statement read:
"This arrest will form part of two ongoing MPS investigations relating to allegations made to police by two separate victims, who made reports of malicious communication to police on 25 and 29 July."
The arrest comes after Labour MP Stella Creasy complained to police after she was threatened with rape on Twitter.
Head of the Association of Chief Police Officers, Chief Constable Andy Trotter has said threatening messages sent via Twitter are "disgraceful" and will be taken seriously by police:
Police are investigating a series of sexually explicit and violent tweets sent to Walthamstow MP Stella Creasy after she spoke out in support of a feminist campaigner who received threats to rape and kill her via Twitter. Scotland Yard said:
Labour MP Stella Creasy has urged Twitter users to block people who send abusive tweets, after she received threatening messages under the hashtag #takebacktwitter.
Twitter's senior director has said the firm are "not blind to the reality" that some users would use the service to post abusive tweets.
Del Harvey admitted that the company could not manually review every tweet due to Twitter's "global reach" but insisted that systems were in place to evaluate violations of rules.
In a statement posted on the website's UK blog, Mr Harvey said: "While manually reviewing every Tweet is not possible due to Twitter's global reach and level of activity, we use both automated and manual systems to evaluate reports of users potentially violating our Twitter rules."
"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."
Mr Harvey stressed that Twitter was continuing to work to make the systems and processes for reporting abuse better.