Maria Miller attended cabinet on Tuesday morningCulture Secretary Maria Miller has said she is "devastated" that she has let her constituents down, amid growing pressure on her to resign.
She told her local newspaper that the 16-month inquiry into her expenses had been "difficult" but she accepted its findings in full and had apologised.
David Cameron has backed Mrs Miller but Tory MPs say the row is damaging.
And former Commons Speaker Baroness Boothroyd has said Mrs Miller should resign as a matter of "honour".
In her first public comments on the issue since she made a much-criticised thirty-two second apology to MPs last week, Mrs Miller, the Conservative MP for Basingstoke, told the Basingstoke Gazette that she had always sought to do the "best job" she could in representing her constituents.
"I am devastated that this has happened, and that I have let you down," she said.
Writing in her weekly column, she added: "I have unreservedly apologised for the way I handled and approached the inquiry.
"And I am pleased that the committee has fully dismissed all of the allegations made against me.
"Separately, I have already apologised and repaid an over-claim of my expenses, having myself drawn the committee's attention to the matter immediately I was aware of it."
The BBC's Political Editor Nick Robinson said he believed the fresh apology was "the minimum requirement" for Downing Street ahead of David Cameron's appearance at Prime Minister's Questions on Wednesday
'Witch hunt'
Mrs Miller was cleared of funding a home for her parents at taxpayers' expense, the central charge against her, following an investigation by the independent parliamentary commissioner for standards.
Mary Macleod: "We can't just let the media do whatever they want"
But the watchdog criticised her "attitude" to the inquiry and recommended she repay £45,000, the amount it believed she had overclaimed in expenses.
The Commons Standards Committee, which the final say on disciplinary matters, disagreed and decided that she had overclaimed by £5,800 and should repay this amount.
This decision sparked a backlash across the political spectrum and calls for changes in how complaints against MPs are investigated.
'Churlish'
Mr Cameron and London Mayor Boris Johnson are among those to have backed Mrs Miller while the minister's parliamentary aide has accused the media of a "witch hunt" against her.
The prime minister is set to face questions about Mrs Miller's future and his handling of the row at a meeting of the influential 1922 committee of Conservative MPs on Wednesday.
The BBC's Political Editor Nick Robinson said he believed the fresh apology was "the minimum requirement" for Downing Street ahead of this meeting and the weekly session of Prime Minister's Questions.
Several Tory MPs have expressed concerns that the saga is proving a damaging distraction as they campaign for local council and European Parliament elections next month.
Baroness Boothroyd, the former Labour MP who was Commons Speaker between 1992 and 2000, accused Mrs Miller of "bringing Parliament into disrepute".
The culture secretary's apology to MPs had not been "very fulsome" and she had dealt with the commissioner in a "churlish" and "legalistic" manner, she told BBC Radio 4's PM programme.
"My concern is that Parliament has taken hard knocks for a long time, and it is now time to try and repair that.
"This does not help at all. I regard it as an error of judgement on the part of Prime Minister David Cameron that he didn't quietly say to her: 'Thank you for your services, but it is time to go.'"
She added: "My concern is with the toxic damage it is doing to the reputation of Parliament. That I feel very strongly about, very clearly about. It is a question of honour, a matter of honour and she should go."
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