Culture secretary Maria Miller has been ordered by the cross-party Commons Standards Committee to repay £5,800 in overclaimed mortgage expenses.
In a damning verdict, the committee accused the cabinet minister of failing to co-operate fully with a 15-month probe into her claims.
Miller said in a statement: "I have accepted the committee's report in full and I will apologise. I am pleased that the Committee has dismissed the allegation made against me by a Labour MP."
Downing Street said she had David Cameron's "very strong and very warm support". The Prime Minister's spokesman said the approach she was taking by accepting the report and apologising was "absolutely the right one".
The culture secretary was however found not to have broken rules by moving her parents into her taxpayer-funded second home.
Miller spoke with the Prime Minister by phone this morning, Mr Cameron's official spokesman said.
The spokesman repeatedly declined to say whether she apologised personally to Cameron or offered her resignation.
He said: "The matter does not arise because she is accepting the committee's report in full, she will apologise to the House. That is absolutely the right thing to do and the Prime Minister is satisfied with that outcome.
"She explained the approach that she was going to be taking. The Prime Minister thinks that is absolutely the right one. What actually was happening is that he was offering her his full, strong, very warm support."
The spokesman rejected suggestions that Miller's ministerial position was more secure because she was a woman - amid criticisms of a lack of female MPs in the upper tiers of Cameron's government. "He would not accept that at all," he told reporters.
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