Liberal Democrat MP Norman Lamb has told the Leveson Inquiry of an "extraordinary encounter" with a News Corporation executive two years ago.
Mr Lamb said he twice met lobbyist Fred Michel in 2010 when he was chief adviser to deputy prime minister Nick Clegg, the Press Association reported.
He said at the time business secretary Vince Cable had responsibility for deciding whether to make a referral of a proposed takeover of BSkyB to the Office of Fair Trading.
Mr Lamb said the takeover topic was raised by Mr Michel at both meetings.
He said a note he took of the second meeting - in October 2010 - contained the words "extraordinary encounter" and "VC refers to Ofcom. They turn nasty".
A lawyer told the inquiry that Mr Michel denied any "express or implied threat".
Mr Lamb said: "The note of the meeting I took is there for all to see. My recollection accords with the note."
He said Mr Michel had "argued strongly, on the basis of the legal position, that there were no grounds for a referral".
"During the discussion he raised the issue of News International newspaper coverage given to the Liberal Democrats," added Mr Lamb in a written witness statement.
"He said he felt that the coverage since the election had been very fair. He specifically mentioned The Sun and indicated that it had given the Liberal Democrats reasonable coverage since the general election.
"He then implied that if the decision surrounding the bid did not fall in their favour, it would be a pity if things were to change and they were no longer able to report in such a positive way.
"I cannot remember the exact phraseology used but the message was very clear. I chose not to respond."
He added: "I was very concerned by what I heard and reported it to Nick Clegg and also to Vince Cable. We were all very clear that nothing of this sort should influence in any way how the bid was considered."