Questions about Maria Miller's expenses have drawn the Culture Secretary into a further row about her office's dealings with the Daily Telegraph, whose investigation led to the commissioner's inquiry.
An aide to Mrs Miller was reported to have called the newspaper and said she wanted to "flag up" the Cabinet minister's connection to press regulation during discussions about a story on the Cabinet minister's expenses.
Downing Street's top spin doctor, Craig Oliver, also mentioned the Leveson press reforms in a telephone call to the Telegraph's editor.
No 10 insisted yesterday that Mr Oliver was highlighting concerns about the way the Telegraph carried out its investigation into Mrs Miller's expenses claims, rather than attempting to threaten the newspaper.
David Cameron gave his backing to Culture Secretary Maria Miller amid the expenses claims.
Asked earlier today at a regular Westminster briefing if the Prime Minister had full confidence in Mrs Miller, a Downing Street spokeswoman said: "Yes, indeed he does."
The expenses investigation facing Maria Miller follows a complaint that she claimed more than £90,000 in second home allowances towards the cost of a house where her parents lived.
The complaint was lodged earlier this week by Labour MP John Mann, who claimed the arrangement was "identical" to that of former Labour minister Tony McNulty.
Mr McNulty was required to pay back more than £13,000 in expenses two years ago, after being found to have effectively "subsidised" his parents from the public purse by allowing them to live rent free in a second home.
Earlier this week Mrs Miller insisted that all of her expenses were "absolutely as they should be" in response to an article in The Daily Telegraph that reported the claims.
Culture Secretary Maria Miller is to have her expenses investigated by Parliamentary Commissioner for Standards John Lyon, his office has said.
Labour MP Simon Danczuk said the Telegraph report about Craig Oliver and Maria Miller contained "serious allegations":
Downing Street defended its communications director Craig Oliver after he raised the issue of Leveson press reforms in a telephone call to the editor of the Daily Telegraph about a story it was planning to run on the Culture Secretary's expense claims.
Mr Oliver reportedly told editor Tony Gallagher "she (Maria Miller) is looking at Leveson at the moment" during the call last Friday.
The Prime Minister's spokesman said: "The Secretary of State had some concerns about the way that investigation was conducted. She set those out in a letter to the editor.
"Craig Oliver was simply reflecting those concerns."
Asked why the issues were brought up together, he said: "I think the point was being made that she had been spending some time in dealing with those issues in recent days.
"But what we were doing was raising some concerns about the investigation on that particular story."
Equalities Minister Maria Miller has postponed planned TV interviews this morning on same-sex marriage.
It comes amid a report in The Daily Telegraph that the Cabinet minister, whose primary position is Culture Secretary, claimed more than £90,000 for a second home where her parents lived.
The Daily Telegraph editor Tony Gallagher has tweeted about the meeting with David Cameron over the Leveson recommendations:
"Beer and sandwiches" is a reference to the refreshments served to union leaders at Number 10 in the 70s.