Tom Crone: 'Quite improper that Mr Watson is sitting on this panel'
News International has complained that an MP involved in a legal row with it should not be allowed to question its staff about phone hacking allegations.
MPs on the culture committee are quizzing the firm's News of the World representatives about the claims.
But its lawyer threatened to complain to the Parliamentary authorities if Tom Watson took part in the questioning.
Labour MP Mr Watson accused the paper of "attempting to interfere with the work of the committee".
The former cabinet office minister began the committee hearing by saying he was being represented by Carter Ruck, the well-known libel lawyers, in a dispute with The Sun newspaper - which is also published by News International.
News International delivered a letter to the committee on Monday evening to object to Mr Watson's presence on the committee.
Its legal adviser Tom Crone said: "Under Parliamentary rules and also the principles, I think, of natural justice and of Article 6 of the Human Rights Act, it seems to us quite improper that Mr Watson is sitting on this panel, dealing News Group Newspapers Limited, with whom he is in litigation.
"If he remains, we will be making a complaint to the Parliamentary Commissioner."
This is not a court, members of Parliament are entitled to express views
Committee chairman, Tory MP John Whittingdale, said advice from the Speaker's counsel was that it did not interfere with his ability to take part in the inquiry.
Later the newspaper's managing editor Stuart Kuttner complained that another MP, Tory Philip Davies, had suggested news that he was to step down from the newspaper was not a coincidence.
He said that bore "no relationship to reality" and his departure had been long planned and suggested Mr Davies was not impartial and should take no further part in questions.
Mr Whittingdale said: "This is not a court, members of Parliament are entitled to express views and it does not in any way disbar them from asking questions in a select committee hearing."
Mr Davies said he had argued in favour of press freedom adding: "It seems quite extraordinary that you should take the view that because I express an opinion with which you are not happy that I should be barred from any proceedings."
The committee is looking into allegations made by the Guardian that "thousands" of public figures, including celebrities and MPs, had their telephone messages hacked into by private investigators paid by the News of the World.
One journalist, former Royal reporter Clive Goodman was jailed two years ago after pleading guilty to hacking into the phone messages of royal staff. Private investigator Glenn Mulcaire was also jailed.
The case led to the resignation of then News of the World editor Andy Coulson, although he said he knew nothing about it but bore "ultimate responsibility" because it happened "on his watch".
He has since become the Conservative Party's director of communications and is also answering the committee's questions about what he knew.
Committee chairman Mr Whittingdale began by saying he had stood aside as a member of the Conservative Party board, which is the employer of Mr Coulson, during the committee's current investigation.
Mr Crone and News of the World editor Colin Myler also confirmed News International had made a payment to Gordon Taylor, head of the Professional Footballers' Association, and two others, which was the basis of The Guardian's phone tapping allegations.
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