Maria Miller, the Culture Secretary and Minister for Women and Equalities, has been ordered to repay £5,800 and apologise to MPs.
The £5,800 is to cover over-claiming of expenses on her mortgage – after she failed to reduce the amount claimed as interest rates and her repayments fell.
However, the Commons Committee on Standards has cleared her of the central charge of deliberately submitting claims for expenses to which she was not entitled.
She is facing calls to resign, but Prime Minister David Cameron has given her “warm support”.
He said: “Maria Miller is doing an excellent job as Culture Secretary and will continue to do that.
“If we look at this report, yes of course these issues do matter – but she was cleared of the original allegation made against her.
“An over-payment was found which she is going to pay back. She’ll make a full apology, and I think people should leave it at that.”
Mrs Miller told the Commons: “The committee has recommended that I apologise to the House for my attitude to the commissioner’s inquiries, and I of course unreservedly apologise.
“I fully accept the recommendations of the committee and thank them for bringing this matter to an end.”
The senior Tory was responsible for steering the government’s same-sex marriage legislation through the Commons.
“I’m very much aware that there are couples who are already in a civil partnership and who may be disappointed that they will have to wait a little longer to be able to convert to a marriage. I’d like to reassure them that we are working hard to ensure that this process is in place by the end of year,” Mrs Miller said.