Jeremy Hunt sent a congratulatory text message to News Corp executive James Murdoch just hours before the minister was asked to oversee the firm's bid for BSkyB, the Leveson Inquiry has heard.
The culture secretary told Mr Murdoch it was "great" that European regulators had decided not to intervene.
Mr Hunt told the inquiry he had been "sympathetic" to the bid, but had "set aside" his views when given the role.
He also denied News Corp had had influence within his office.
Downing Street later said the prime minister believed Mr Hunt had acted properly when he was responsible for the bid for the satellite broadcaster and would not be referring his case to the adviser on the ministerial code.
"Jeremy Hunt set up a process which left him with a 'vanishingly small' chance to 'manipulate' the bid for 'political or other ends'," a spokesman said.
Labour has argued the culture secretary should stand down, claiming he was in breach of the code for failing to supervise his adviser over his contacts with News Corp and for misleading the Commons.
His adviser Adam Smith resigned last month after admitting that his frequent contact with the company was inappropriate.
The current phase of the inquiry into media ethics is examining the relationship between the press and politicians.
The decision to ask Mr Hunt to oversee the BSkyB bid came in December 2010, after Business Secretary Vince Cable was stripped of the responsibility for telling undercover journalists he had "declared war" on News Corp chief Rupert Murdoch.
Mr Hunt said he would not have sent the text to Mr Murdoch, which said "Great and congrats on Brussels. Just [regulator] Ofcom to go", had he known he would be given responsibility for the bid later that day.
Labour MP Chris Bryant told the BBC David Cameron should sack Mr Hunt because he had been texting James Murdoch despite telling Parliament he had had no direct contact with News Corp over the takeover.
But Conservative MP Louise Mensch said "he has been completely exonerated today".
The inquiry heard on Thursday that:
- Mr Hunt considered resigning, but added: "I had conducted the bid scrupulously fairly... I decided it wouldn't be appropriate for me to go"
- He said sending replies to text messages from James Murdoch was "courteous", adding he would probably now "avoid all text messages"
- Mr Hunt's special adviser Sue Beeby told him he should not to have a drink with No 10 director of communications Andy Coulson after he left Downing Street until the bid process was over, as Mr Coulson - an ex-News of the World editor - was considered to be so close to News International
- He revealed he uses his personal email account to conduct government business, with his departmental account run by staff who alert him to anything significant
- Special adviser Adam Smith sent Mr Hunt a text telling him Rebekah Brooks had resigned as chief executive of the company. He replied immediately saying: "About bloody time!"
The "great and congrats" message was one of a number Mr Hunt exchanged with James Murdoch on the afternoon of 21 December 2010.
Mr Hunt also sent a text to Chancellor George Osborne expressing fears the government would "screw up" over its handling of the BSkyB bid as a result of Mr Cable's comments.
He also said he had had a phone conversation with James Murdoch on 16 November 2010 - before he began overseeing the bid - to hear what was "on his mind at that time" and considered that "appropriate" behaviour.
And referring to a memo on the bid that he sent to Mr Cameron that month, Mr Hunt said that "apart from informing the prime minister of my views I wasn't actually doing anything about it".
"It was widely known that I was broadly sympathetic towards the bid," he added.
On the moment the bid decision was handed to him, Mr Hunt told the inquiry: "I believe I did totally set aside all those sympathies."
Mr Hunt said claims made on 4 July 2011 that murdered schoolgirl Milly Dowler's phone had been hacked by the News of the World - part of the News Corp empire - had made him re-evaluate the News Corp bid. In the days after the revelation, it was announced the newspaper was being shut down.
He denied having been pressured by Number 10 to ask Ofcom and the Office of Fair Trading to re-examine the bid, saying the decision had been his own.
"I asked myself, if they found it necessary to close down the whole paper... is there a corporate governance issue here?" said Mr Hunt, who supplied the inquiry with 160 pages of memos, emails and text message transcripts.
On 11 July, News Corp abandoned its takeover bid for BSkyB amid outrage over the phone-hacking scandal.
'Very heavy heart'
Asked earlier by Robert Jay QC, counsel to the inquiry, about comments on his personal website which said he was a "cheerleader for Murdoch", Mr Hunt said it had been a comment in a press article and not how he would describe himself.
Mr Hunt defended his special adviser's contact with News Corporation lobbyist Frederic Michel, saying he was "totally shocked" by the volume of contact from Mr Michel, and describing one particular text as "pushy" and "cheeky".
He said Mr Smith's role had been as "an official point of contact" with News Corp but that he did not speak on his behalf.
"What Mr Smith hasn't done, as far as I can tell, is ever go back and agitate for the thing Mr Michel is putting him under pressure to achieve," said Mr Hunt.
He said he accepted Mr Smith's resignation over the level of contact with a "very heavy heart", and "personally found the whole thing very difficult" but felt the result was inevitable.
"I do feel that the bid was conducted completely fairly. What we didn't predict was the pressure that Adam Smith was going to come under," he said.
He also admitted he had a mobile phone conversation with James Murdoch on 16 November 2010 to hear what was "on his mind at that time" and considered that "appropriate" behaviour, despite legal advice not to have external discussions about the bid.