MPs Tom Watson and Louise Mensch have clashed on Twitter over the anti-Rupert Murdoch commentary made in a select committe report on phone hacking.

The outspoken Labour and Conservative members first publicly clashed when the culture, media and sport select committee published its report into News Corps handling of the phone hacking scandal but have continued their fight on the social media tool with tit-for-tat tweets.

The committee's report concluded that the committee had been "misled" by News Corp and News International representatives, before claiming that Murdoch was "not a fit person to exercise the stewardship of a major international company".

When the report was published it was revealed that the committee was split down party lines over the rhetoric of the report, with Watson leading the Labour charge for the strongest criticism of the media tycoon.

Mensch made it clear during the conference that she believed the report had lost some of its impact for "partisan party politics" after the Conservatives were out-voted by six to four as sole Liberal Democrat Adrian Saunders, voted with Labour.

Watson and Mensch, have since continued their disagreement on Twitter. Watson launched the first blow, criticising Mensch for not making her lack of support clear before the day of the report being published.

"Amendment was in on 27th March. You waited until Monday [30 April] to say you wouldn't support report if it was included," he tweeted.

Mensch responded: "You never discussed it nor asked for it to be discussed. All Conservative members were stunned to find you pushing it - and Lab voting."

Watson replied: "Why did you say that? Now you've broken the convention, are you happy for me to publish the amendments you withdrew?"

Mensch said she was happy for him to do so, before claiming: "[You] don't convict based on some gut feeling - there was no, zero, evidence".

She said she believed that the committee's conclusions were outside its remit and a matter for Ofcom, a response shared by Labour leader Ed Miliband.

The continuing disagreement risks stealing the focus from the report itself, as its impact is diminished by the lack of a unanimous decision. Concerns have also been raised that its controversial commentary, branded "completely ludicrous" by Tory committee member Phillip Davies, simplified the issue and this diminished the impact of accusations it made for which it had clear evidence.

Many critics of Mensch's position on the report abused her on Twitter, causing her to publish a number of particularly foul-mouthed examples to highlight the misogyny faced by female politicians.

In an interview with BBC Radio 4, she said: "It's not Twitter's fault. Twitter provides a social media platform, it's the fault of the users.

"They have to be responsible for their own words and what they say."