David Cameron did not seek further assurances from his communication chief in 2009 that he had no links to the phone hacking scandal at the News of the World, despite fresh allegations in the press.

Speaking at the inquiry into press standards and media ethics on Thursday, Andy Coulson, the former Downing Street communications director, was asked if the prime minister had asked him to confirm he knew nothing of phone hacking while he was editor of the tabloid.

"Not that I can recall," Coulson said.

Coulson, who became Cameron's communications director in 2007, quit his Downing Street post in 2011 under mounting pressure about his involvement in the scandal.

In July 2009 Coulson came under pressure to resign his job with the Conservative Party after the Guardian reported that the News of the World and other newspapers hacked the phones of public figures.

Coulson told the Leveson inquiry that when Cameron hired him in 2007 he had asked him about the arrest of Clive Goodman, the NotW's royal corespondent, over phone hacking.

However according to Coulson, the then Tory leader did not think it necessary to seek further assurances following the Guardian's explosive revelations in 2009.

And he was given Cameron's full backing, who said he believed in giving people a "second chance".

At the inquiry today, Coulson was also asked about Cameron's admission last July that politicians and the media had become "too close".

The former journalist said the Premier had not expressed similar regret in private before that.

"I don't remember him doing so," he said.

Cameron "frequently" expressed frustration about the amount of time he needed to spend with figures from the media.

Questioned on whether he had seen any contacts he regarded as too close, Coulson responded: "I look at it from the perspective of whether or not there were improper conversations.

"I never saw a conversation, was party to a conversation, that to my mind was inappropriate in that way."

In his written statement, Coulson said he did not think at the time that there was any conflict of interest in taking the communications job.

He had sold all shareholdings in News International by May 2010. But he accepted there was a potential conflict with restricted stock in News Corporation that he was granted as part of his severance package.

That stock "vested" in August 2010 and is worth around £40,000 - although Coulson stressed that he did not know the value while he was working for Downing Street.

"Whilst I didn't consider my holding of this stock to represent any kind of conflict of interest, in retrospect I wish I had paid more attention to it," he said in his statement.

"I was never asked about any share or stock holdings and because I knew that I wasn't involved in any commercial issues, including the BSkyB bid, it never occurred to me that there could be a conflict of interest."

He said he was not involved in the News Corp BSkyB bid "in any way, shape or form", and could not remember dealing with communications issues from it, except the Daily Telegraph's revelation that Business Secretary Vince Cable suggested he was "going to war" on Murdoch.

Earlier in the testimony, Coulson said that he told David Cameron and George Osborne that his News International background "could not be seen as a factor" in guaranteeing the support of those newspapers after he had been recruited by the Conservative Party.

On Thursday, Lord Rothermere, the owner of the Daily Mail, gave evidence to the inquiry, as did John Mullin, the former editor of the Independent. Mullin was forced to explain his decision to publish a story about Coulson that contained details from his witness statement to the Leveson Inquiry.

During the opening of the third module of the inquiry, dealing with relations between media figures and politicians, Jay suggested that Rupert Murdoch had suffered "selective amnesia" when he claimed to have forgotten a key lunch with Margaret Thatcher.