The centre-right candidate for the French presidency, François Fillon, has apologised over payments made to family members for parliamentary work, reports the BBC.
He said that although the practice was legal, French people no longer accepted it and that he had made a "mistake".
Mr Fillon's campaign has been dogged by claims, which he denies, that his wife and two of his children were paid for non-existent parliamentary work.
Some in his party, the Republicans, feel he should step aside.
Recent polls have suggested that he may be eliminated in the first round of the presidential election in April, paving the way for a possible run-off between centrist Emmanuel Macron and far-right leader Marine Le Pen.
But speaking to reporters in Paris, Mr Fillon insisted that he would stay in the race.
He said he had acted legally, had "nothing to hide", and that both his wife and children had done vital work when he was a member of parliament.
Mr Fillon also said he would publish details of his assets on his website and propose reforms on rules regarding parliamentary work.
He added: "What was acceptable in earlier times no longer is. By working with my wife and children, I was mostly mindful of this relationship of trust, but today this causes mistrust. It was a mistake. I regret it profoundly and I apologise to the French people."
Mr Fillon, a 62-year-old former prime minister, has consistently denied wrongdoing since the allegations surfaced last month.
Media reports said his wife, Penelope Fillon, earned €831,400 (£710,000; $900,000) as her husband's parliamentary assistant between 1998 and 2012, and questioned how much work she had done.