Conservative chairman Grant Shapps said it was time to "draw a line" under the controversy over Culture Secretary Maria Miller's expenses, as Labour called on David Cameron to show "leadership" over the affair.
Pressure on the Culture Secretary was stepped up by the release of a recording of a phone call between her special adviser and a reporter investigating her expenses claims. The tape revealed that Jo Hindley "flagged up" the fact that Mrs Miller would be discussing the Leveson report on media standards with the paper's then editor Tony Gallagher - something Mr Gallagher said he regarded as a threat.
Meanwhile, the former chairman of Westminster's independent sleaze watchdog, the Committee on Standards in Public Life, said Mrs Miller's failure to co-operate fully with the parliamentary standards commissioner's inquiry was "pretty shocking".
Letters released yesterday showed that the Culture Secretary told commissioner Kathryn Hudson that a decision to uphold the complaint against her would be "irrational, perverse and unreasonable... a decision that no reasonable decision-maker could properly reach" and warned that she could go over her head to the committee of MPs which has the final say on standards issues.
Ms Hudson eventually recommended that Mrs Miller should repay £45,000 in expenses for a house which she shared with her parents, but the cross-party Commons Standards Committee overruled the commissioner and decided she only needed to hand back £5,800. The committee did criticise Mrs Miller for failing to co-operate with the inquiry, and she was forced to make a humiliating apology to the House of Commons.
Former CSPL chief Sir Alistair Graham told the BBC Radio 4 Today programme: "The degree of lack of co-operation or the attempt to divert the commissioner from addressing the issues concerned seems fairly exceptional. I think particularly for a senior Cabinet minister, who you expect to show a leadership role in co-operating with whatever expenses system is around, it is pretty shocking.
"I think the public will be very shocked that the committee did overturn one of the key recommendations about how much should be repaid back, when there is a real possibility that the minister made a capital gain with the help of public funds."
But Mr Cameron has made clear that he supports the Culture Secretary - though he did not name her in a list of Cabinet ministers singled out for praise in a speech to the Conservative Spring Forum.
Mr Shapps said there was nowhere left for the case against Mrs Miller to go.
"The main accusation was thrown out," the Tory chairman told the BBC. "There was a matter for which she's apologised - partly the amount of time it took to get the information together. She's apologised to Parliament and, as the Prime Minister said today and yesterday, that does rather draw a line under it.
"Maria Miller has entirely accepted (the committee's) recommendations, she's come to Parliament and done that. The Prime Minister has accepted that. It doesn't seem to me there's much other place for it to go."
Labour backbenchers have urged police to examine Mrs Miller's expenses and demanded the publication of the full minutes of the committee's meetings to discuss the case behind closed doors.
And the party's shadow leader of the Commons Angela Eagle said: "The latest revelations and the release of a recording raise further serious questions for Maria Miller and David Cameron.
"They urgently need to make clear what they knew about these calls and what action they took about them.
"There is also the important question of whether there has been a breach of the code of conduct for special advisers or the ministerial code.
"It is time for David Cameron to show some leadership, stand up and say that what has happened was wrong and to answer these questions in full."
In the audio tape released by the Telegraph, Ms Hindley tells the reporter that another journalist who called at Mrs Miller's home had spoken to the MP's father, who had recently been in hospital. Some details were redacted from the recording to protect his privacy.
"I should just flag up as well, whilst you're on it, that when she doorstepped him, she got Maria's father, who's just had a (redacted) and come out of (redacted)," said Ms Hindley.
"Maria has obviously been having quite a lot of editors' meetings around Leveson at the moment. So I'm just going to flag up that connection for you to think about."
Explaining why he regarded the reference to Leveson as a veiled threat, Mr Gallagher told BBC2's Newsnight: " The press was feeling very vulnerable just after the publication of the Leveson Report and there was a great desire on the part of all media organisations not to fall foul of somebody raising the spectre of Leveson.
"We were in no doubt that threats were being made."
But a Whitehall source said that it was clear from the recording, made without Ms Hindley's knowledge, that she had been voicing concerns about the doorstepping of Mrs Miller's father, and had been making clear that the minister would raise the issue at an upcoming meeting with the editor, which happened to relate to the Leveson report.
Emails released by the Standards Committee showed how Mrs Miller told Mrs Miller that she might have to refer her inquiry " to the supervisory jurisdiction of the Standards Committee" .
In another message, she wrote: "In light of the evidence that is before you ... to continue to regard this spurious complaint as a serious matter would give it credence it does not deserve and undermine the inquiry process in comparison to issues that really are serious matters."
John Mann, the Labour MP whose complaint sparked the Commissioner's investigation, said: "These emails show that Maria Miller bullied and threatened the independent Commissioner.
"This is a gross abuse of her position as a member of the Cabinet. This issue alone warrants her resignation or immediate dismissal."
Deputy Prime Minister Nick Clegg declined to come to Mr Cameron's aid over the Miller affair, telling Sky News: "All the issues to do with her position and indeed to do with the behaviour of her office, alleged or not, is entirely a matter for the Prime Minister.
"It's quite right for me to leave the Prime Minister to make those decisions, and indeed to speak for himself."
Mr Shapps said he did not believe Ms Hindley's reference to Leveson amounted to breach of the special advisers' code of conduct, which requires them to conduct themselves with integrity.
The Tory chairman told Channel 4 News: "The truth of the matter was that an elderly man in his 70s who was in a fragile condition was doorstepped. I think that was the concern, in the context of Leveson, which looked at intrusion into the privacy of ordinary individuals. I think it was in that context.
"We know that the facts of the matter are that somebody who was a member of the public, effectively - Maria Miller's elderly father is exactly that - was approached in circumstances which were not ideal.
"I think it's true to say that at the time there was some acceptance that, had they have known, that approach wouldn't have been made. I think that was the point that was being made."
On Mrs Miller's dealings with the commissioner, Mr Shapps said: "This was something that went on a very, very long time - well over a year - that asked lots of detailed questions, and in the end Maria used a solicitor and oftentimes with solicitors it all becomes a bit legalistic.
"I don't want to get into the semantics of which words should have been used. The simple fact of the matter is that Maria has accepted in her statement to Parliament that this perhaps could have all been handled much faster. I'm sure she was frustrated that it hadn't been and that's why she said she of course unreservedly apologised.
"This has been now very thoroughly investigated in a huge amount of detail, every aspect of it. It's come to a conclusion... It's happened now, she's made an apology and the Prime Minister has said it draws a line under it, and that's of course what it does."
The watchdog in charge of MPs expenses said that the House of Commons should give up the power to police itself over standards and ethics.
Sir Ian Kennedy, chairman of the Independent Parliamentary Standards Authority (Ipsa), said that "MPs marking their own homework always ends in scandal".
Parliament should end the system under which a cross-party committee of MPs is able to overrule the findings of an investigation by the standards commissioner, he suggested.
Sir Ian - who has led Ipsa since it was created to reform expenses in the aftermath of the 2009 scandal - told the Sunday Times: "We have made great progress in cleaning up the problems of the past. To avoid further damage to Parliament in the future, it should have the confidence to give away powers in regulating itself and see that independent regulation is the best, most transparent way forward.
"MPs marking their own homework always ends in scandal. It happened with expenses. It will happen with standards investigations too. Ipsa has shown that independent regulation of parliamentary behaviour can work. Our reforms have cleaned up the system."
MPs should "learn a lesson" from the independent regulation of expenses and ensure that Ms Hudson too is " given the freedom to carry out her work and not have her wings clipped by MPs", said Sir Ian.