MPs will write to News International chairman James Murdoch to press him further on claims that his company snooped on them when they were pursuing allegations of phone hacking, a senior parliamentarian told Reuters on Wednesday.

James Murdoch, son of News Corp chairman Rupert Murdoch, appeared before a parliamentary committee for a second time last week to testify about phone hacking at the company's now-defunct News of the World tabloid newspaper.

Murdoch apologised when asked about reports that the newspaper had placed committee members under surveillance, including Tom Watson, one of its most vocal critics.

But Culture, Media and Sports committee chairman John Whittingdale said he wanted more information.

The committee takes very seriously allegations that members were under surveillance by reporters in the course of our inquiries. Obviously this is something we want answers to, he said.

We will be writing to James Murdoch as head of News International to confirm or deny the allegations and would also write to other Murdoch executives involved, he told Reuters.

They will be asked whether the allegations are true, and if so, how many of the committee were placed under surveillance, when, for how long, and who authorised it.

(It) raises very serious questions about a potential attempt to interfere with the work of a committee of parliament, Whittingdale said.

Committee member Therese Coffey said members felt extremely uncomfortable at the thought that they and their families could have been followed. It's another page in the saga of this inquiry, she said.

The phone-hacking scandal has raised doubts among shareholders over whether James Murdoch is the right person to succeed his father as head of the News Corp global media empire.

Murdoch junior is the chairman of News International, the company's British newspaper arm, and also chairs the pay-TV operator BSkyB, in which News Corp is the biggest shareholder.

Committee member Louise Mensch asked Murdoch last week about reports of snooping on MPs by private investigators.

I am aware of the case of the surveillance of Mr Watson; again, under the circumstances, I apologise unreservedly for that, Murdoch told the parliamentary committee.

It is not something that I would condone, it is not something that I had knowledge of and it is not something that has a place in the way we operate, he added.

The hacking scandal has shaken the British establishment, raising questions about the way the media operate and their relations with the police.

An inquiry set up by Prime Minister David Cameron began this week following a public outcry after it emerged that the News of the World had hacked the phones of murder victims, as well as large numbers of celebrities.

(Writing by Keith Weir and Avril Ormsby; Editing by Tim Pearce)